Post on 07-Apr-2018
transcript
8/3/2019 030 - Paper
1/45
Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in
Chinas Housing Market
Yongheng Deng and Peng Liu
First Version: October 2005This Version: March 2007
Keywords: Mortgage, Prepayment, Default, Credit Risk, Forward Contract
JEL Classification Number: G12, G14, G21, H31
Contact author: Peng Liu, F605 Faculty Building #1900, Haas School of Business, University of California, Berkeley,CA 94720, Tel: 510-6438543, Email: peliu@haas.berkeley.edu; Yongheng Deng, University of Southern California,School of Policy, Planning, and Development, 650 Childs Way, RGL 201A,Los Angeles, CA 90089-0626, Tel: 213-821-1030, Email ydeng@usc.edu. We thank Mark Carhart, Pierre Collin-Dufresne, Tom Davidoff, Kent Daniel, RobertEdelstein, Dwight Jaffee, John Quigley, Richard Stanton, Adam Szeidl, Sheridan Titman, Nancy Wallace and seminar
participants at Cornell University and U.C. Berkeley for helpful comments. All errors are ours.
8/3/2019 030 - Paper
2/45
Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in
Chinas Housing Market
ABSTRACT
Forward housing market, which enables the consumer to lock in future housing price, is verycommon in Asian countries. Most condominiums in China are sold forward on a pre-sale market,where purchasers and developers transact at the date of pre-sale on an underlying property, whichis not yet completed. During the pre-sale period there is significant default risk of developers.However home buyers can borrow mortgages from banks so that they can share the forwardcontract risk with the banks. This explains the phenomena of irregularly high early stage defaultand prepayment rates observed in residential mortgage lending in China where there is little or nofinancial incentives for mortgage borrowers to exercise either put or call options. An investor(home buyer) in Chinas forward housing market will choose to default her mortgage contract ifthe developer defaults the forward housing contract. If forward house is delivered, the investor
may choose to prepay the loan depending on her liquidity constraints and returns in alternativeinvestment channels.
Mortgages collateralized by forward housing asset are riskier than those with underlyingassets traded on the spot market. However, currently the Chinese mortgage banks charge the samerate to all mortgage borrowers. This results a cross subsidization between mortgage borrowersgroups in the forward and spot housing markets. Cross-subsidization, where one group pays arelative high price and thus enables another group to pay a relatively low price is pervasivephenomenon in both product market and financial market. This paper uses a rich set of data froma leading mortgage lender in China. The loan history data set contains not only mortgage loancharacteristics, but also borrowers and developers information. The unique data set allows us to
study the mortgage borrowers prepayment and default behavior with embedded forward contractrisks. The finding of this study will provide valuable insight about emerging housing andmortgage markets in China as well as those in other transition economy.
8/3/2019 030 - Paper
3/45
1
1. INTRODUCTION
The residential mortgage market in China has grown rapidly since 1998 with an average
annual growth rate of roughly 100%. By the end of first quarter of 2005 the outstanding balance
of residential mortgages reached 1.7 trillion RMB Yuan, approximately $207 billion US dollars.
1
There are two highly distinctive features of the Chinese mortgage market: first, the Peoples Bank
of China (the Central Bank) set a uniform mortgage rate which is applied to all types of
borrowers. There is a long history of not using risk-based interest rates in China or other central-
planning economies. It is also a tradition that in those countries a unified product or service is
provided to all consumers. Second, beyond the standard spot market for housing transactions,
there is an active forward real estate market in the sense that the developer can sell housing unit
before its completion, sometimes even before construction begins. During pre-sale period there is
significant default risk of developers. However, the home buyer in China is allowed to borrow a
standard mortgage from a bank to finance the pre-sale unit. As a result, home buyers in the pre-
sale housing market can share the forward contract risk with the banks. This explains the
phenomena of irregularly high early stage default and prepayment rates observed in residential
mortgage lending in China where there is little or no financial incentives for mortgage borrowers
to exercise either put or call options. An investor (home buyer) in Chinas forward housing
market will choose to default her mortgage contract if the developer defaults the forward housing
contract. If forward housing unit is delivered, the investor may choose to prepay the loan
depending on her liquidity constraints and returns in alternative investment channels. Because of
the embedded risk of developer default, the mortgages collateralized on pre-sold property are
more risky than their counterparts on the spot market.
This paper studies the competing risks of mortgage prepayment and default with
embedded forward contract risk of developers default. The economic model is based upon Cox
proportional hazard model (Cox, 1972, 1975) of mortgage termination. The empirical analysis is
based upon a rich set of mortgage lending data from a leading mortgage lender in China. The loan
history data set contains not only mortgage loan characteristics, but also borrowers and
developers information. The unique data set allows us to study the mortgage borrowersprepayment and default behavior with embedded forward contract risks. The finding of this study
will provide valuable insight about emerging housing and mortgage markets in China as well as
those in other transitional economy. The remainder of the paper is organized as follows. Section 2
describes the Chinese mortgage market in detail, including both the single mortgage rate
1As of March 2007 the exchange rate of Chinese Yuan (CNY)is one U.S. dollar = 7.74 CNY.
8/3/2019 030 - Paper
4/45
2
constraint and the forward market for new units. Section 3 describes the data used in this study.
Section 4 lays out the empirical methodology. Section 5 presents a discussion of empirical results.
A brief conclusion follows.
2.THE MORTGAGE AND REAL ESTATE MARKETS IN CHINA
There is long history of Real Estate market and consumer loan market in China before
1949, when China adapted the central planning system after the Communist Party took over. The
earliest real estate transaction can be traced back to 20 BC, Eastern Han Dynasty 2 . Before
adapting the central planning system in 1949, active real estate and mortgage markets had already
existed in China especially in big cities, such as Shanghai and Beijing. For a long period of time
under central planning regime, housing in China had been social welfare product administrated
and delivered by state agencies (e.g. state-owned enterprises and housing bureaus) for its people.
Under such a welfare-oriented system, a private housing market and housing mortgage system
extinguished. The mission of Chinese Banks was to act as a government directed funding source
for SOEs.
Since the early 1980s, China has gradually restructured its housing system. Market
mechanisms, with the objectives to eliminate state housing allocation, promote privatization of
public housing and encourage private housing development, were introduced in stages to replace
the welfare housing system. Although China's first modern residential mortgage loan was issued
in 1986 by China Construction Bank (CCB), the mortgage market did not play an important role
in the Chinese residential housing market for another decade. By the end of 1997, the total
outstanding mortgage balance in People's Republic of China was only approximately 19 billion
RMB Yuan (USD $2.35 billion). In 1998, the People's Bank of China, which functions as the
central bank of China, and the State Council of China announced several administrative laws to
speed up housing construction and intensify urban housing reform. Among them, the State
council announced that it would no longer allow state-owned enterprises (SOEs) to allocate
welfare housing to their employees after December 31, 1999. Since then, residential mortgage
lending began to accelerate. By the end of 2005 the outstanding balance of residential mortgages
exceeded two trillion RMB Yuan (USD $198 billion), an increase of 40% compared to the 2003
balance, and almost 89 times the1997 balance. Residential mortgages play an increasingly more
important role in Chinese banks' lending activities. The outstanding mortgage balance constitutes
2The Cambridge History of China Volume 1, The Chin and Han Empires P666, Edited by Denis Twitchett andMichael Loewe.
8/3/2019 030 - Paper
5/45
3
more than 12% of total loans made by financial institutions in the same period in 2005, compared
to less than 0.4% in 1997.
[Insert fig. 1]
Although mortgage lending currently constitutes about 85% of total consumer lending(no credit card loans and very few automobile loans are issued by banks in China), the ratio of
mortgage loans to total loans is 7.5% lower than most developed countries (e.g. the ratio of
mortgage to total loan is 39% in U.S. and 59% in U.K.), and even lower than other countries in
the Asian-Pacific region (e.g. the ratio in Hong Kong, Taiwan, Singapore, Malaysia and Korea
was 34%, 30%, 27%, 26% and 23%, respectively) . Therefore there is much room for continuing
growth in China' mortgage lending.
[Insert fig. 2]
[Insert fig. 3]
[Insert fig. 4]
The Institutional Background of Residential Mortgage Lending in China
The current residential mortgage market in China is dominated by four major state-owned
banks. They account for more than 90% of the total outstanding mortgage balance. Of these four
banks, Industrial and Commercial Bank of China (ICBC), and China Construction Bank (CCB)
are the two leading mortgage lenders, representing about 70% of total outstanding mortgage loans.
Currently there are four categories of residential mortgages in China: (1) individual
account housing loans, (2) individual provident fund housing loans, (3) combined housing loans,
and (4) second-hand housing loans. Individual account housing loans is the most common form
of individual household mortgage loans. CCB Individual provident fund housing loans are
housing loans using provident funds that bank operate on half of institutions that manage the
funds. Usually individual provident fund housing loans enjoy a lower mortgage rate than
individual account housing loans. The current spread is 44 basis points. Combined housing loans
refer to loans granted to individual home buyers, using both bank's funds and provident fund as a
source of funding. Second-hand housing loans are loans that facilitate individual purchases in the
secondary housing market.
Mortgage application requirements
8/3/2019 030 - Paper
6/45
4
The loan amount shall not exceed 80% of the purchase price or the appraisal value,
whichever is lower. That is 20% of the purchase or maintenance price, is reserved for the down
payment. The applicant should provide acceptable statements of stable income and payment to
income ratio should not exceed 70%. The mortgage term shall not exceed 30 years. Other
required documentations include personal identification, purchasing contract, title to the property,
appraisal report, housing (pre-)sale permit, banking statement, proof of stock and bond
investments, etc.
Payment methods
If the loan term is one year or shorter, both principal and interest must be repaid as a
lump sum at maturity; if the loan term is longer than one year, the loan may be repaid in equal
installments of the principal plus interest, or in equal installments of principal. The borrower may
choose either method, but there may be only one payment method for each loan, and after the
method is specified in the contract, it may not be changed.
Mortgage Interest Rates and Adjustment
The mortgage rates that banks charge to customers are regulated by Peoples Bank of
China (PBC), the central bank of China. All banks follow the same lending rules. Currently the
mortgage interest rates is 4.77% for individual account housing loans with a term of five years or
below; for loans with a term above five years, the interest rate is 5.04%. The spread between the
long term (more than 5 years) and short term (5 years or less) is 27 basis points. The individual
provident fund housing loans is 3.6% and 4.04% for term below 5 years and above 5 years
respectively. All residential mortgages in China are adjustable rate mortgages (ARMs). During
the loan term, the interest rate may change according to what is set by the People's Bank of China
(PBC). Once the new mortgage rate is announced, the rate will be applied to all mortgages.
Default Risk Management
Currently Chinese banks use a five-category system to manage default risks of mortgageportfolio. The five default risk categories areNormal, Alert, Irregular, Distress, and Default.
Before approval of a loan, the bank investigates the credit worthiness of each individual
applicant. The bank will approve a mortgage to an applicant according some borrower
characteristics like family income, occupation, etc. Therefore there are only two pre-lending
classes: Normal for better credit loans and Alert for good credit loans. The bank watches the
8/3/2019 030 - Paper
7/45
5
borrowers' payment behaviors very carefully and makes frequent adjustments to the borrowers'
risk level if they see any warning signal. Specifically, if the number of delinquencies is between 3
and 6, mortgage borrower's risk level becomes Irregular; if the number of delinquencies is above
6 then borrower's risk level becomes Distress. The last category in the five-category risk level is
Default. The headquarter of any mortgage lending bank also actively monitors its branches and
subsidiaries. An early warning is given to the branches with 1% to 3% delinquency rate in their
mortgage loan portfolio; the headquarter requires a reorganization of mortgage operations at
branches whose delinquency rate falls between 3% to 5%; the mortgage lending license would be
revoked if a branch has more than 5% delinquency rate.
Real Estate Developers and Strong Secular Growth Trend in Housing Demand
Real estate development was a highly regulated industry in China before 1992. With the
privatization of state owned housing and the fast growth of mortgage lending, real estate
developers in china begin to flourish. There are currently more than four thousands active real
estate developers in Beijing. Before 1992 there were only 37 state-owned real estate developers in
Beijing. With an average increase of 50 developers a year, the total number of developers until
1997 was 335. The total number of developers doubled in 1999 and structure of developer
became diversified. With the stimulation of mortgage lending activities, the average annual
growth rate jump to 96%, the total number was 548 in year 1998, 1023 in year 2000 and 1979 in
year 2002 respectively. In addition to the housing reform, China's capital market begin to grow,
with the recent reform such as apparition of Chinese currency Yuan and further opening of
financial market to foreign banks as required by the WTO. Moreover the most recent financial
innovations such as real estate investment trusts (REITs) and mortgage backed securities (MBS)
all start from the real estate finance sector, the emerging and fast-growth capital market in China.
The on-going process of these reforms has translated into a booming domestic property sector and
acceleration in residential housing investments in recent years. As a consequence, the share of
residential housing investment as a percentage of GDP has risen to 5.6% in 2003, up from less
than 1% before the 1990s.
Notwithstanding fast industrialization, the degree of urbanization, as measured by the
ratio of urban residents to total population, is exceptionally low in China. Industrialization
without urbanization is a unique Chinese phenomenon, owning to decades of government policies
that segregated urban and rural labor markets. The pent-up urbanization demand, evident from the
acceleration of rural migration, has also coincided with the unleashing of pent-up demand for
8/3/2019 030 - Paper
8/45
6
improving housing conditions nationwide. The average per capita housing area in square meters
for both urban and rural residents has jumped from7-8 sq. m. in 1978 to above 20 sq. m. in recent
years. We believe the evolution of consumer demand is heavily influenced by income distribution
and the emergence of the middle class, because at a different income levels, different projects
become affordable and available. Experiences in other economies have shown that as annual
income crosses US$ 3,000 per capita; there is a period of rapid expansion in the size of the
middle class and acceleration in consumer demand. Figure 5 shows the decreasing nationwide
trend of supply to demand ratio indicating the strong secular growth trend in China's housing
demand.
[Insert fig. 5]
The Forward (Pre-Sale) Housing Market in China
The majority of residential housing units in urban China are condominiums, and most
condo purchases are transacted on the forward market. A forward sale is also called pre-sale. In
2003, more than 80% of projects initiated a pre-sale according to a survey. Condo developers
usually sell their projects well before completion, usually two to three years,3 in order to hedge
the housing price and get additional funding. On the transaction date, home buyers (mortgage
borrowers) have to pay purchase price in full on a development that is not completed. To share
the risk of developer default, home buyers (mortgage borrowers) usually fund the housing
purchase by putting a down payment of 10% to 30% and borrow a 20 year mortgage4 from a bank
that charges the same adjustable mortgage rate. The mortgage provides the borrower embedded
options to default and prepay the loan at any point before loan maturity. Even though banks pool
forward and spot contracts in real estate market by charging the same rate, one should realize that
the market structure leads to very different option exercise behaviors for the two types of
borrowers. The collateralized borrowing based on the presale units introduces additional risk for
mortgage default and prepayment. The developer asks for the full purchase price at presale day,
the mortgage loan serves partially as consumption insurance. If the developer defaults on the
forward contract, the borrower defaults on her loan. (The loan is non-recourse in China).
Presale does not only exist in China, it is a popular practice in other markets as well. In
most Asian markets: Hong Kong, Taiwan, Singapore, Japan and in some European countries, like
Russia, Italy, Span forward housing sales are very active. The presale practice is also active in the
3The presale period used to be around 4 years, but now decreased to one to two years.4 Sometimes shorter maturity of 15, 10 years mortgages is borrowed with different rate.
8/3/2019 030 - Paper
9/45
7
U.S. condominium market, especially in large cities. In United States, pre-selling of buildings and
resort condominiums (Miami, Hawaii, for example) has become a standard process, and virtually
every condominium is pre-sold today.5 The procedures of forward presale contract can vary from
country to country, and from developer to developer in the following dimensions: length of
presale period, size of down-payment/deposit, payment schedule, refund policy in case of the
developer default, and eligibility of mortgage loan and mortgage rate. In Hong Kong, the
common practice is that the developer must complete a certain percentage of the development
before the government gives the presale consent. In the U.S., China and Singapore for example,
the forward sale can take place after developer getting construction permit and before
construction starts, thus the name pre-construction. For example in Florida developers need pre-
construction sales of 50% to 90% of the units before they can borrow funds to begin construction.
While in Singapore and China the entire purchase price is required to be paid at the time of
presale contract is signed; a sequential payment schedule is contracted in U.S. For most Florida
condominium developments, investors need only deposit 10% of the presale price at contract time,
a second 10% after 3-6 months or when developer breaks ground. For most condo presales in
U.S., the deposits are held in escrow. The investors can get full refund in the case of developer
defaults.
Despite the differences in the contractual details of forward presales, there is a common
risk that associated with all forward contracts: the counterparty default risk. On the forward
housing market, all investors are well informed of the possible failure of delivery on the
contracted houses. Because the investors are buying something that does not yet exist, there is a
greater potential for unforeseen problems and setbacks to occur before the investor move into her
home. The need not be built disclaimer gives the developer protection from suits of
nonperformance if the developer does not proceed with the construction. However there may be a
significant social loss in the sense of incomplete structures that arise from developer default.
When the presale was first used in China around 1998, majority of developers are state-owned
and completion of the development was perceived by forward contract purchasers as guaranteed
by government. As the housing demand is so high and real estate development is such a profitable
industry, more and more private companies came into the market. With uncertain construction
cost, the developers then have incentives to exercise their default option. This introduces
inefficiency for there would be social waste resulting from uncompleted projects. The Chinese
5Sample of pre-sale contract can be found in Miami real estate website. www.miamirealestatetrends.com
8/3/2019 030 - Paper
10/45
8
government has realized the problem incentive-compatible mechanisms are under consideration
beyond reputation and regulation rules.
The convoluted relationship among the developer, home buyer and mortgage lenders can
help to explain two paradoxes in China mortgage market: why the prepayment rate is high in the
adjustable rate mortgages where there is no incentive to refinance? Why the default rate is also
high in a period of a booming housing market? We will explore the phenomenon and
explanations in more detail in the empirical modeling session.
3.THE DATA
Micro Mortgage Loan Data
The unique micro mortgage dataset collected by the largest residential mortgage lender in
Beijing, China was first used by Deng, Zheng and Ling (2005). In this paper we enriched the
dataset in several dimensions. We updated the mortgage loan data to the end of 2003.
Furthermore we extended the loan information to include the property information and developer
characteristics. This second extension is crucial because those variables enable us to merge
borrowers characteristics of loan with the collateral information from developers in Beijing. The
loan dataset includes 103,462 individual mortgage loans issued between 1998 and 2003. The
mortgages are 5 year, 10 year, 15 years and 20 years adjustable rate loans with level payment. For
each loan, the available information include the year and month of origination and termination (if
it has been closed), indicators of prepayment or default, original loan amount, down payment rate,
initial loan-to-value ratio, maturity, remaining term, repayment method, mortgage contract rate,
the purchase price of the property, size of the house, location of property, sale type, appraisal
value of property at time of sale, unit price, etc. Other borrower characteristics include borrower
name, education, gender, monthly income, occupation and position, number of dependents in the
household and income from spouse. The dataset also has geographical information of the property
and its developer. This micro loan data is well suited for the study of mortgage default and
prepayment, since Beijing is the capital city of China and the real estate sector is steadily
increasing without speculative bubble. Among the 103,462 mortgage loans, 1,384 loans were
defaulted and 10,055 loans were fully prepaid during the sampling period, and 92,023 loans were
censored at end of year 2003. This data is best for survival analysis because the data avoid the
truncation and censoring problems. The sample started from 1998; which is the first year the bank
issue mortgage loans. There is no left truncation problem as most research has in sample selection
8/3/2019 030 - Paper
11/45
9
process. The data collection cutoff date is December 31, 2003. Therefore the right censoring is
non-informative6.
Tables 1-5 provide the descriptive statistics of the mortgage loans. Among 103,462
residential mortgage loans originated in Beijing, more than 74% are based on forward contracts.
Among 1,384 defaulted loans, and among 10,055 prepaid loans, more than 90% are from forward
market. The borrowers behavior in default and prepayment vary by loan characteristics like LTV,
original loan amount, and borrowers income, occupation and other household characteristics. In
addition, borrowers behavior in default and prepayment vary by developer characteristics like
type, size, quality, history, etc. For example, about 45% defaulted loans are originated on the
properties built or to be built by joint developers with partners in Hong Kong, Macau or Taiwan
(HMT thereafter); while only 5% from joint developers with partners in foreign countries. Within
all prepaid mortgages, 47% are based on properties built or to be built by limited companies;
while only 2.5% are by joint venture with HMT. Among the 103,462 mortgages, more than 63%
loans are originated on a property which is the first project by its developer. Only 34% are by
developers who have built more than one project in the past. The detailed descriptions can be
found in table 1-4.
[Insert Table 1]
[Insert Table 2]
[Insert Table 3]
[Insert Table 4]
[Insert Table 5]
Developers Credit Risk Data
Another dataset used in this paper is credit rating data of real estate developer in Beijing
from Beijing Urban Construction Development Office (BUCD thereafter). BUCD is a
government agency regulating real estate industry in Beijing. In 2004 BUCD begins to annually
review all real estate developers in Beijing and publish the results on its official website. With
growing concern about information disclosure of developer credit record, BUCD also has built a
6An alternative sampling method, namely stratified sampling mechanism can be used for a large dataset. To correctthe possible sample selection bias, a weighing scheme which is assumed to be independent of error distribution can beused in the maximum likelihood estimation. Specifically, the weight addresses the stratified choice-based sampling ofmortgage .les across loan status cells. The weight is commonly defined as the inverse of the probability that the loan is
being selected from a cell where was sampled.
8/3/2019 030 - Paper
12/45
10
credit database of real estate developer for public inquiry. This dataset include 3,088 developers
and 3,938 real estate development projects in total.
Among all developers, about 87 percent of developers only have one property in Beijing;
only 3% of the developers have 4 properties or more. The earliest developer in our sample, a state
owned enterprises (SOE), started its real estate business in 1966. There was no big growth in real
estate sector since then. In 1992 the total number of developers was only 90, the number
Quadrupled in 1997 to 335. Since then real estate development industry has experienced a
significant growth. By the end of 2003 the total number of developers was almost ten times the
number in 1997.
For each developer in the sample, we have information of credit ratings from real estate
administration office and commercial banks, type of developer, equity value of firm at
registration, location of properties and business address of developer, name of CEO and legal
person, total number of employees and detailed number of certified professionals in the
management. We also have the issuance and expiration date of license, starting date in real estate
business.
4.THE EMPIRICAL MODEL AND ESTIMATION METHODOLOGY
4.1 AN ECONOMIC MODEL OF MORTGAGE PREPAYMENT AND DEFAULT WITH EMBEDDED
FORWARD CONTRACT RISKS
A Simple Model for Forward Housing Market
The presale practice, adapted from Hong Kong and other Asian markets created a
forward market in Chinese residential housing market. Similar to financial instruments, investors
can buy real estate either on a spot market or on a forward market. On the spot market, investors
and developers transact on existing housing units - housing stock; while on the forward real estate
market, the investors and developers agree on the price at the date of sale but the underlying
property, which is not completed yet, is transferred to the buyer only at a certain period later,
usually at the date of completion. Because the unit is sold well before completion and occupation,
the forward contract is often called a pre-sale or pre-construction.
[Insert fig. 6]
Figure 6 uses a simple timetable to illustrate the interrelationship between the home
buyer (mortgage borrower), the developer and the bank on the forward housing market.
8/3/2019 030 - Paper
13/45
11
Following Liu (2007), we set up a three period model, the agents only make decisions at discrete
time at T = 0, 1, 2, 3. T=1 is completion / delivery date of housing units. Home buyer (mortgage
borrower) can enter the housing market either at time T=0 (spot market) or at T=1 (forward
market). Therefore the transaction date can be either at T=0 or at T=1. At the transaction date, the
home buyer has to pay the developer the full purchase price on the housing unit and the home
buyer is eligible to borrower an adjustable rate mortgage from the Bank. The mortgage loan is
usually less than 80% of the housing value, which means that the purchaser only put down
payment of 20%. The mortgage matures at T=3, but the borrower can terminate the loan at any
time. For simplicity, we assume the borrower only terminate the loan at T=1, 2, 3. The developer
and the bank have an agreement so that the developer deposits the proceeds into the bank at
transaction date. Between time 0 and time 1, there is a pre-sale period, in which the developer
sells housing units forward before completion of the project. At T=1 of the forward market, there
is a probability of developers failure of delivery of the unit, which results in default of the
mortgage. In the case of default, the bank takes the collateral residuals, which typically have very
low recovery rate currently in China. If the housing unit is delivered in good quality, the home
buyer (mortgage borrower) starts to consume the housing consumption. T=2 is the option
exercise date for a home buyer (mortgage borrower) who is consuming a housing service and
pays a monthly interest and principal of mortgage. She would default if the value of the house is
lower than the value of the debt borrower from the Bank. She would prepay if the financing cost,
i.e. the mortgage interest cost, exceeds the alternative investment return. The borrower may not
optimally prepay the mortgage if she is financially constrained, either due to liquidity constrain
(the borrower does not have enough cash to pay off the loan) or she does not participate the stock
market investment. Therefore if the home buyer (mortgage borrower) does not terminate the
mortgage, at T=3 she makes the last payment and obtained the title of the house.
There are at least two main advantages for home-buyers to lock into a pre-sale contract
before the construction of the property is completed. First the housing price in the pre-sale market
is typically lower than that on the spot market. Second there may be richer menu of choices:
location, size, view, etc. For developers, there are two benefits associated with pre sale contract.
First, by locking in the selling price, the developer can hedge the project pipe line risk and share
the risk with buyers. The uncertainty about future demand and inventory risk is significantly
reduced. Secondly the developer can access additional zero cost financing in addition to
construction loan which is typically very difficult for private developer to apply from the banks.
For new developers, presale funding may be the only source of capital for construction.
8/3/2019 030 - Paper
14/45
12
In China and other emerging markets, home buyers typically lose all the down-payments
in the case of developer defaults. However currently Chinese home buyers can borrow a certain
amount of mortgage loans from banks, and furthermore they benefit the same mortgage rate as
spot market investors. A condo purchaser can default the mortgage loan, if developer fails to
deliver the unit according to the presale contract. Because of the popularity of the forward
housing market and the practice of the risk sharing mechanism adopted by the home buyers
(mortgage borrowers) in China, the risks in the forward real estate market have been embedded
into the mortgage contract default risks, which makes the valuation of the mortgage default and
prepayment option value becomes more complicated than those in other countries.
Default Option with Embedded Forward Contract Risks
The option theory (Black and Scholes, 1973 and Merton, 1973) has been widely applied
to estimate the mortgage default and prepayment probability. Early examples include Findley and
Capozza (1977), Buser and Hendershott (1984), Brennan and Schwartz (1985) among others.
Recent applications include more sophisticated modeling techniques (see, for example, Schwartz
and Torous, 1989, Stanton, 1995, Deng, Quigley and Van Order, 2000) and more realistic
assumptions (see, for example, Quigley, 1987, Quigley and Van Order, 1995, Archer, Ling and
McGill, 1996, Calhoun and Deng, 2002). However this method was developed and first used in
developed mortgage market in which spot housing contracts are predominant. Understanding of
forward housing market and its option structures are necessary in order to apply the option theory
to the mortgage pricing in which the forward selling is active. Under the forward contract when
buyers borrow mortgages from bank and start to pay back amortized loan amount, they have not
seen their house yet. With astonishing growth in real estate market, many private developers enter
the residential housing market. There is increasing default risk among developers that fail to
deliver the house. Many Chinese borrowers use the mortgage as a consumption insurance
instrument to share the credit risk of developer with banks. In case the borrower did not get the
desired home, i.e. the developer defaults or fails to satisfy the home buyer on the date of delivery,
the borrower defaults. On the other hand, if the borrower gets a house of good quality, she will
not default, and will consider prepaying according to borrower's liquidity constraint and other
investment opportunities. For example, if borrower can earn a higher return from other
investment portfolio (from stock market or bond market), even though the borrower has cash on
hand - not liquidity constrained, she rather not prepay the mortgage. However if other investment
opportunities give her lower return then mortgage rate and If the investor is not constrained, she
will pay off the loan. Although in reality investor has to evaluate the option value of waiting, the
8/3/2019 030 - Paper
15/45
13
prepayment option basically reflects the trade-off between financing cost (mortgage rate) and
alternative return, as well as liquidity constraint of the borrower.
This forward-selling practice is quite common in other developing countries or
transitional economies as well, where there is high demand in residential housing and the
governments encourage consumer lending to stimulate real estate construction. The increased
leverage via pre-sale then increases credit risk of developer which will be eventually transferred
to house buyers. It is rational for the buyer to borrow mortgage loan from a bank, thus sharing the
housing-consumption risk. On the demand side, since the commercial housing market is relatively
new, there may simply not enough desirable housing on the secondary housing market. Besides,
recognizing that the banks charge the same mortgage rate, pre-sale mortgage borrowers implicitly
get a cross subsidy from spot market borrowers.
The Default and Prepayment Option Analysis on the Forward Market
Due to the pre-sale feature, the mortgage options are different from the ones in the spot
market. Because all the current mortgage contracts in China are Adjustable Rate Mortgages
(ARMs)7 and the mortgage rates are not indexed to any rate, but imposed by the central bank. We
found that pre-sale practice in China's housing market plays a crucial role in mortgage defaults
and prepayments. An important reason why people want to borrow money from a bank is to
facilitate a housing consumption. Since they face tremendous risks when developers fail to
deliver properties on the contracted delivery date or fail to meet the quality requirements
specified in the pre-sale contracts. Here house refers to all kinds of housing units in China's
residential housing market, most of them are condominium, and some are not. In our sample
period, every year there are more than five hundred of new properties in Beijing. (Note: most
housing units are condos in which one property could have tens of thousands units). The
sophisticated borrowers use the mortgage as a consumption insurance instrument to share the
credit risk with banks. If the borrower had a bad draw, i.e. the developer defaults, the borrower
also defaults. On the other hand, if the borrower has a house of good quality, she will not default,
and will consider prepaying according to borrower's liquidity constraint and other investment
opportunities. There are two important institutional issues that permit such a risk sharing behavior.
Firstly residential mortgages in China are non-recourse; and secondly, so far there is no personal
credit system in China, and banks dont share mortgage borrowers information. These features
are especially common in transitional economies or developing countries.
7See Stanton and Wallace (1999) for a discussion of application of option theory to the adjustable rate mortgages.
8/3/2019 030 - Paper
16/45
14
Before the discussion on how to calculate the value of default and prepayment options,
further understanding the details of those options and how they differ from their U.S. counterparts
are needed. In China, a housing unit can be purchased on either the spot market, where the house
has been built, or on forward market (pre-sale), where the building has not been completed yet.
Although fundamentally different, (a specific housing unit cannot be simultaneously on both the
spot market and on forward market at the same time), the purchase and financing procedures are
exactly the same. Consumers have to pay in full using either own equity or mortgage or a
combination of both on the transaction date instead of forward delivery date. Mortgage lenders
charge the same rate to the borrowers. For the pre-sale house, the borrower can default on a
mortgage loan at delivery day. It is essentially a European put option. On delivery day, there is a
probability of developer default, hence failure of delivery of a contracted house. Mortgage default
can be of two reasons during pre-sale period. The first is from the credit risks of developer. These
risks include market risk (via a channel of construction cost) and the idiosyncratic risk of the
individual developer. The second risk is from the borrower. An individual borrower can have a
negative income shock or other unplanned event (e.g. a big expenditure on medical care). Since
during the pre-sale period, the borrower cannot borrow from other places and cannot re-sale the
house (due to its adverse selection problem), they will lose the house and payments made earlier
plus the down payment if they default before the maturity. Knowing this, a rational borrower will
keep enough funds for the mortgage payment beyond the down-payment during pre-sale period.
For simplicity, we assume the borrower only exercises the put option on the delivery date.
Therefore the mortgage partially serves as consumption insurance instrument. A borrower wants
the protection from the credit risk of developer or qualifies of house.
At the delivery date, the mortgage options for pre-sale and non- presale becomes identical.
After the pre-sale period, the borrower can default or prepay on the mortgage. Mortgage default
option can be regarded as a financial put option. If the current market value of the house, which
serves as collateral on the mortgage debt, drops below the current value of the remaining
mortgage balance, a borrower has an incentive to default. In a boom market, the default option is
usually out of the money. Borrowers would be better off by selling the house, rather than default,
if they have to move. On the other hand, the prepayment option is a real option (call) with strike
price updating every year (depending on bank ARM rate). This call option is does not depend on
interest rate, but is closely related to the borrower's alternative investment set. One can think of
mortgage debt as a consumption smoothing instrument. In the current Chinese capital market,
there are very few investment opportunities, and very few borrowing vehicles. For example there
are no credit card loans and other consumer loans are very limited. The mortgage market is a
8/3/2019 030 - Paper
17/45
15
major and steady growing sector in Chinese debt market; while the stock market is the major
investment sector. Therefore borrowers will make prepayment decisions based on cost of capital
and stock market return. They will prepay when the cost of capital (mortgage rate), exceeds
investment return. Figures 7-8 show the mortgage rate dynamics and stock index return in China
during period of 1998 2005. The optimal stopping time of prepayment depends on borrower's
income and her judgment about stock market return and interest rate in the future. If borrowers
are the same, i.e. they have same income flow, same information, same perception of macro
economy, and same risk aversion, they will prepay at the same time.
[Insert fig. 7]
[Insert fig. 8]
In most developed economies, researchers model mortgage contract in a contingent claim
framework. The borrower's option to prepay the mortgage is an embedded call option at a strike
price of par while the default option is a put option at a strike price equal to the market value of
the collateral property. The prepayment option gives a mortgage borrower the right to repay the
mortgage balance when its market value equals or exceeds par, i.e. the market rate drops below
the mortgage coupon rate. Exercise of the call option results from two primary motivations: (1) to
refinance the existing debt at a lower rate of interest; and (2) to terminate the debt through sale of
the underlying asset house, due to relocation for example. However China's mortgage
prepayment behavior contradicts to the conventional wisdom in the existing literature which
considers the financial call option value of prepayment as an important factor. Because all the
current mortgage contracts are ARMs (see Cunningham and Capone, 1990, and Stanton and
Wallace, 1999, for a discussion of modeling the termination risks of ARMs). Furthermore, the
mortgage rates are not indexed to any rate, but extraneously imposed by the central bank.
An analog to prepayment, in U.S., mortgage default is regarded as a financial put option.
If the current market value of the house, which serves as collateral of the mortgage debt, drops
below the current value of the remaining mortgage balance, a borrower has an incentive to default.
Therefore the default may be viewed as a put option that gives the borrower the right to sell the
house to the lender at a price equal to the value of the mortgage. In the absence of transaction
costs, a rational borrower can maximize her welfare by exercising the options when they are in
the money. From a quick glance at China's housing prices, one can easily conclude that the
housing market is booming and the financial put option is far out of the money. Then what makes
the Chinese borrowers default or prepay their mortgage loans is puzzling.
8/3/2019 030 - Paper
18/45
16
In this paper, we rationalize borrowers' behavior by realizing that the motivation of
mortgage borrowing is partly because of risk-sharing and partly due to liquidity constraints. We
found that the prepayment and default are closely related to the quality of the underlying property
or the credit risk of the developer. Since in our study all the defaulted loans involved a developer
with only one property for sale on the market; therefore, determining the default risk of mortgage
borrower is equivalent to predicting the credit risk of the developer company.
We also find that pre-sale practice in China's housing market play a crucial role in
mortgage defaults and prepayments. An important reason why people want to borrow money
from a bank to facilitate a housing consumption is that they are facing tremendous risks in the
case that developers fail to deliver the properties on the contracted delivery date or fail to meet
the quality requirements specified in the pre-sale contracts. However the house buyers have to
take the risk, since there are simply not enough existing houses on the market. In our sample
period, every year there are about 555 new development offered in Beijing. (Note: most housing
units are condos in which one property could have tens to thousands of units) on the market.
There are two important institutional issues that permit such a risk sharing behavior. The
residential mortgages in China are non-recourse; so far there is no personal credit system in China,
and banks don't share mortgage borrowers' information.
4.2 THE COMPETING RISKS HAZARD MODEL OF PREPAYMENT AND DEFAULT
The default and prepayment are options of borrowers embedded in any mortgage loans.
Recent research on mortgage markets indicates that exercise behaviors of those two options are
distinct but not independent. For example, exercising the default option, the borrower gives up
the option to prepay the loan in the future. We apply the Cox proportional hazard model to assess
the competing risks of mortgage termination by simultaneously modeling the prepayment risk and
default risk.
Since the early work of Dunn and McConnell (1981), Green and Shoven (1986),
researchers have modeled mortgage contracts in a contingent claims framework. The borrowers
option to prepay the mortgage is an embedded call option at a strike price of par while the default
option is a put option at a strike price equal to the market value of the collateral property. The
prepayment option gives a mortgage borrower the right to repay the mortgage balance when its
market value equals or exceeds par, i.e. the market rate drops below the mortgage coupon rate.
Exercise of the call option results from two primary motivations: (1) to refinance the existing debt
at a lower rate of interest; and (2) to terminate the debt through sale of the underlying asset, the
8/3/2019 030 - Paper
19/45
17
house, due to relocation reason for example. In analogy to prepayment, mortgage default is a put
option. If the current market value of the house, which serves as collateral of the mortgage debt,
drops below the current value of the remaining mortgage balance, a borrower has an incentive to
default. Therefore the default option gives the borrower the right to sell the house to the lender at
a price equal to the value of the mortgage. In the absence of transaction costs, a rational borrower
can maximize her welfare by exercising the options when they are in the money.
As discussed in the section above, the special features of Chinas mortgage contract have
to be taken into account when calculating the option values. Specifically the collateral of pre-sale
house has to be carefully modeled for default option; while prepayment option is different in an
economy where there is essentially no interest risk. The prepayment option is at work, even
though there is no interest risk, because mortgage borrowers the will decide when to exercise
based on the trade-off between borrowers financing cost and alternative investment returns.
Furthermore, these two options compete against each other. Kau et al (1992, 1995) have
discussed the theoretical relationships among the options. Schwartz and Torous (1993) is among
the first to demonstrate the empirical importance.
The desired model outputs are explanatory variable effects on conditional probabilities of
mortgage default or prepayment. We estimate a proportional hazards model (PHM) which
estimates the effects of theses variables on the time to default. In particular, we estimate the
probability that a mortgage with certain characteristics will terminate in a given period where
there has been no default or prepayment experience up until that period.
Following Deng, Quigley, and Van Order (2000), this paper simultaneously estimates the
competing risks of mortgage defaults and prepayment. The joint survival function is given in the
following form:
}),,,(exp{)(
}),,,(exp{)(
where
}exp{
},,,,,,|,Pr{
),,,,,,|,(
2'
1'
0
2'
1'
0
11
ppBCpkppkpk
ddBCdkddkdk
t
k
pk
t
k
dk
pdBCppdd
pdBCpd
ZXXRHgthh
ZXXRHgthh
hh
ZXXRHtTtT
ZXXRHttS
pd
++=
++=
=
>>=
== (1)
The log integrated hazard function can be also written in the following form as:
8/3/2019 030 - Paper
20/45
18
jBCjjjjjjBCjjjj XXRHgIIZXXRHglh +++++= ),,,(),,,( 432'
10 (2)
In this formulation, Sis cumulative survival probability conditional on housing priceH,
alternative investment returnR , vector of macro-economic variablesZ and vector of micro
variables ),,,( BC XXRHg . Both Z and g are time-varying, where Z measures the systematic
risk of the market and loan level information g measures the intrinsic values of the default and
prepayment options. Among g, BX represents borrower characteristic and cX stands for
collateral information. Ij is a dummy variable equal to unity if the loan is to finance a forward
house, and zero otherwise. dT , pT are discrete random variables representing the loan life of a
mortgage prior to default and prepayment respectively. hik ; i = d; p are hazard functions;
Unobserved error terms associated with the hazard functions for default and prepayment are
denoted by d , p respectively to represent heterogeneities. The Kaplan-Meier approach was
used to fit the empirical hazard rates of prepayment and default based on the entire sample.
However equation (2) assumes that the market effects of Z are the same for both forward
mortgage and spot market mortgage. It also assumes that the error structures are the same for all
mortgage loans. To accommodate this restriction, a more complete separation regression for
forward market and for spot market can be estimated similar to Blinder (1973) and Oaxaca (1973).
For Spot market without pre-sale
S
j
S
jj
SjjBC
Sjjj
Sj
G
ZXXRHglh
+=
+++=
),,,( 2'10(3)
For Forward market with pre-sale
F
j
F
jj
F
jjBC
F
jjj
F
j
G
ZXXRHglh
+=
+++=
),,,( 2'
10(4)
where ]'),,,([ ' ZXXRHgG BCji
j = is a column vector of repressors; j = d; p and i =
S; F ; jjj 2'
10 = , jjj 2'
10 = are regression coefficients.
The log Hazard Ratio, denoted by LHR between two groups of F and S can be
decomposed into two parts.
8/3/2019 030 - Paper
21/45
19
)()(
+=
=
FSF
SF
j
GGG
GGLHR(5)
where the upper bar associated to a variable indicates the mean and estimated coefficients. The
first part of risk differential is due to differences in the typical loan characteristics of forward
versus spot )( FjF
j GG , assuming they are valued at the same spot market. The second part of
the risk differential reflects the portion of the higher risk on forward market loans that arises
because they are priced differently than otherwise identical mortgages for existing house
financing.
The default options in pre-sale period versus post-sale period are total different. In the
post-sale period the default option is related intensively to the housing price. However in the pre-
sale period, the default option is mainly depend on the probability of default of developer.
Following Deng, Quigley and Van Order (2000), the proxy values of exercising the put option
for mortgage borrower in post-sale period is measured by the probability of negative equity.
Typically one cannot estimate directly to which the default option is in the money without
knowing the entire path of individual house values. However, we can use the initial loan-to-value
ratio and the diffusion process of house prices to estimate the critical value for borrower exercise
of put option, known as the probability of negative equity. Specifically, the variable put_proxy
is defined as:
))loglog(Put_Proxy
Hr VVN = (6)
Where
= +
+
+=
kT
ii
k
kr
r
MV
1 )1(
(7)
)(
H
HPV kH
+= (8)
Vr is the market value of mortgage debt; M is monthly payment of mortgage principle
and interest, kr+ is adjustable mortgage rate for loan originated at time and after the seasoning
period of k. T is the mortgage term. VH is the market value of the house which is purchased at
with price P and valued at +k ; H is housing price index at time in the area. The term in
parentheses of equation (8) follows a log normal distribution. )(N is the cumulative standard
8/3/2019 030 - Paper
22/45
20
normal distribution function, is housing index volatility8. The calculation of Vr is a little
complicated. It involves firstly calculate annually re-setting monthly payment of principle and
interest.
The intrinsic value of call option is defined as:
r
Rr
V
VV =Call_Proxy (9)
where Vr defined previously is the market value of mortgage, the cost of financing a
house purchase, and VR is the value of a hypothetical income, the return from alternative
investment.
Since stock market is a major investment alternative, the Shanghai stock price index is
used in return calculation. Specifically, VR is defined as:
=
++
+
+=
kT
ii
f
i
KkR
r
RMV
1 )1(
)1( (10)
In addition to intrinsic value of options, three sets of non-option related variables are
included in the regression. Those variables include time varying and time invariant determinants
of mortgage performance motivated by recent research. The first set of variables, denoted by XB,
describe the borrowers characteristics, including gender, age, education, log value of monthly
income from borrowers and their spouses, occupation, marital status, number of dependents in
borrowers household, etc. The second set of variables, denoted by XC, describes the collateral
information. The developer related information includes credit ratings, type of developer, age of
the developer, equity value of firm at registration, size of developer, ratio of certified
professionals to total employees, and number of projects, etc. Other loan related information
includes original loan amount, down payment rate, loan-to-value ratio at origination, year and
month, maturity, size of the house, location of property, sale type, appraisal value of property at
time of sale, unit price, etc.
5.EMPIRICAL RESULTS
The risks analyses are based on the full sample from the combined dataset of bank loans
and real estate developer credit database. The competing risks of default and prepayment are
8The housing price indices and their volatilities are estimated according to the three stage procedure originally createdby Case and Shiller (1989) and modified by Quigley and Van Order (1995).
8/3/2019 030 - Paper
23/45
21
estimated jointly. Table 6 presents three variations of the competing risks model of loan
termination. All specifications incorporate both market variables and a rich set of loan
characteristics including borrowers characteristics and collateral information. The market
variables include time-varying proxies for local economic conditions, such as inflation,
unemployment rate, the slope of term structure of interest rate, stock market returns, etc. Each of
the three models contains separate flexible baseline functions for default and prepayment that
follow Han and Hausman (1990). Model 1 tests both default rate and prepayment rate equations
following equation (2) where the presale dummy is estimated in hazard regression framework and
the interaction term 4 is constrained to be zero. Further, the model does not control directly for
the intrinsic value of call and put options in the estimation. Model 1 provides a benchmark for the
competing risks specifications discussed below. Model 2 extends model 1 by including the
contemporaneous values of options in both default and prepayment equations. Model 3 further
extends model 2 by including interaction terms of presale with call option and put option in both
risk equations. Overall, the competing risks models are well-specified and control for
approximately 40 different characteristics of the loan, borrower and collateral characteristics and
market information.
[Insert Table 6]
As evidenced in model 1, estimation results indicate that economic conditions of the
market have important impacts to default and prepayment behaviors. As a proxy for overall
economy, the Shanghai Stock Index is negatively associated with default and prepayment. The
increase in local unemployment rates positively affects the exercise of the default option and
prepayment option. This result is highly significant across model specifications. Unemployment
rate is a macro variable indicating the strength of the macro economic environment. It also
reflects Chinese borrowers confidence about the job-stability and financial soundness. For most
Chinese households, housing is a basic consumption. When facing uncertainty about future
wealth, they will choose to invest in housing, rather than risky stocks and bonds. This is quite
different from US, where prepayment risk is negatively associated with unemployment rate. The
slope of term structure of interest rate, defined as the difference between the five year CD rate
and spot rate disclose the expectation of future interest rate. When the yield curve becomes fatter,
borrowers in China may prefer to prepay the mortgage debt. As show in model 1 while the
relationship between default behavior and slope of term structure is statistically insignificant, the
prepayment rate is negatively associated with the slope of term structure and statistically
significant.
8/3/2019 030 - Paper
24/45
22
The estimates from model 1 suggest that the loan to value ratio at origination is positively
associated with default risk and negatively associated with prepayment risk. Higher LTV reflects
that the purchaser is more liquidity constrained and has less equity invested in the house. Model1
also shows that the likelihoods of default and prepayments vary positively with housing-expense
burdens proxied by mortgage expense to income ratio.
Model 1 also estimates the affects of borrowers characteristics, including borrowers age,
sex, marital status, education background, occupation and job positions, log monthly household
income and number of dependents in the household. Among these categorical or continuous
variables, household income is an important factor in determining default and prepayment risk.
High income borrowers are less likely to default and more likely to prepay. The log income is
highly significant across 3 models. Another continuous covariate that is statistically significant is
number of dependent in a household. The more the dependents in the household, the higher
burden of the mortgage borrower, thus the higher the default probability and the lower
prepayment risk. Among the categorical covariates, the sex is insignificant; age is significant
among these 3 models. Older borrowers have relatively lower default risk and higher prepayment
risk. As younger people in China are more liquidity constrained and also prefer to smooth
consumption by borrowing, reflecting a difference in lifestyle preference in China. Marital status
is another significant factor in determining default rate and prepayment rate. Married borrowers
have both lower default rate and prepayment rate reflecting that a family is a more stable and
responsible social unit than singles. Occupations and job positions are significantly associated
with prepayment risk. Business and Trade industry shows higher prepayment risk due to their
relatively volatile income streams, while research and education sector has lower risk of
prepayment because of the nature of relatively stable income streams. Managers exhibit relatively
higher prepayment risk than technicians and self-employee. On the other hand, none of them is
statistically significantly associated with defaults. Borrower with college degree has lower default
risk but higher prepayment risk.
In addition to borrowers characteristics, model 1 also finds significant impact of
collateral information to mortgage termination in China. Specifically, mortgages with underlying
property built by bigger or older developer exhibit lower default risk. There are two measures of
developer size, one is currency adjusted value of registered equity, and the other is total number
of employee in the firm. These two size variables are all statistically significantly associated with
default risk, while the association with prepayment risks is insignificant. New developers tend to
associated with higher default risk and higher prepayment risk of mortgage loans. In the sample
8/3/2019 030 - Paper
25/45
23
period of the study, Chinese housing sector is experiencing tremendous development which
triggers more company enter into real estate business. While it is hard for the investors to monitor
and judge the quality of the property they are developing, established developers have operational
advantage in this market. Not only the developer quality affect property price, but also have
impact to financial market via the channel of mortgage termination. The developers who involved
in residential real estate development for more than 20 years are associated with lower default
risk and higher prepayment risk. The ratio of certified professionals to total employee of the
developer is also significantly associated with mortgage default and prepayment rates. The higher
the professional ratio is associated with lower default risk and higher prepayment risk. A strong
developer tends to have more certified professionals and have passed higher industry standard
(for example ISO9000) and also prefer to take long-term commitment. Since a developer with
good quality tends to have better cost management, quality control and reputation concern, its
presale house will have higher probability of failure of delivery. Therefore the mortgages
associated with good quality developers will have lower default risk and higher prepayment rates.
The type of developers also associates with different default risk and prepayment risk. The
foreign joint venture developer exhibits lower default risk and higher prepayment risk, while the
joint venture with Hong Kong, Macao and Taiwan developer are associated with higher default
risk. Comparing with State-Owned developers, the private developers and limited company have
both higher default risk and higher prepayment risks. The location of property is also associated
with different default and prepayment risks. In central city area, due to competition and tighter
regulation or monitoring, mortgages with underlying property in central city area tend to have
lower default risk and higher prepayment risk.
Model 2 extends model 1 through the introduction of the option-related time-varying
covariates into both the default and prepayment equations.9 The estimates confirm that the put
option, measured as the probability of negative equity, is positive and highly significant in the
exercise of the default option; the call option value is also positively and highly significant in the
exercise of the prepayment option. In other words, increase in the probability of negative equity,
the incidence of default increases dramatically. On the other hand, declines in returns from
alternative investment that bring the call option "in-the-money" will lead to a high prepayment
activities. Stock market in China is a fast growing investment vehicle beyond traditional deposit.
Investment in stock market has been attached more and more importance in Chinese peoples
financial decision. The intrinsic value the prepayment option basically reflects investors portfolio
9 Log Likelihood and Schwarz-Bayesian Criterion (SBC) reported at the bottom of the table provide comparison of thegoodness of .t among alternative models. Models with lower values are considered preferable.
8/3/2019 030 - Paper
26/45
24
choice. Model 2 further indicates that a value of call option is negatively associated with default
risk. In a bull stock market, household may relocate their asset from housing to stock market by
stopping mortgage payment.
Model 3 further include the interaction term between presale and option values to test
whether the intrinsic value of options in forward market have different influence than on the spot
market. The default behavior is less sensitive to the put option and call option for mortgage loans
with pre-sale properties. For prepayment behavior, the call option and put option are less sensitive
to pre-sale mortgage loan borrowers. This means that the pre-sale in apparently an important
factor that highly correlated with default risk and prepayment risk. If the loan is associated with
forward housing purchase, it is such a bad news for default and prepayment risks that option
value (both call and put) do not add as much to the risks as in spot market. The significance in the
product terms indicate that the default risk and prepayment risks exhibit quite differently in
forward market for the pre-sale houses than on spot market.
In a similar fashion, product terms between presale and other borrower characteristics
and collateral information can be tested. Since mortgages on presale houses exhibit strikingly
different default and prepayment behaviors, a more complete separation of hazard regressions are
performed towards forward market and spot market respectively. Table 7 displays the regression
results for the two markets. On forward market, while intrinsic value of call option is significant
for exercises of default option and prepayment option, probability of negative equity is associated
with neither default option nor prepayment option in statistical sense. The value of mortgage
default option has totally different underlying among pre-sale houses, versus completed projects.
On the forward market, housing price index has little to do with default risk, since the collateral
for presale houses is on paper. Therefore the probability of negative equity is more closely
associated with houses on spot market, while houses on forward market depend more on
probability of house delivery. Another remarkable feature on the separate regressions is that
borrowers characteristics and developer information play different roles on spot market versus
forward market. The borrower characteristics (age, marital status, education, occupation and job
position) are only statistically significant on spot market, not significant on forward market. On
the other hand the developer characteristics (number of projects, size, type and history of the
developer) are only statistically significantly associated with mortgage termination for presale
loans, none of them is significant on spot market. For example, younger borrowers, singles,
elementary school education group and clerk, social service as well as self-employment group are
associated with higher default risk, while older borrowers, singles, college education and
8/3/2019 030 - Paper
27/45
25
managers are associated with higher prepayment risk. However none of these borrower
characteristics is statistically associated with mortgage termination risks on forward market. On
the other hand, good credit quality of developer, e.g. completed more projects in the past, bigger
and experienced developers, higher ratio of certified professional to total employee, foreign joint
ventures, is associated with lower default risk and higher prepayment risk. None of these
developer characteristics is statistically significant in the spot market regression. Although the
sensitivities are different, some loan variables, location variable and market condition share the
same sign across the spot market and forward market. For instance, on both markets, the more
dependents in a household, the higher the default risk, the lower the prepayment risk due to
households liquidity constraints. Central city location enjoys lower default risk and higher
prepayment risk.
[Insert Table 7]
To demonstrate the mortgage prepayment and default risks with and without embedded
forward contract risks, we simulate 300 paths of house price appreciation rates and stock returns
according to a joint stochastic mean-reverting process. These 300 randomly sampled paths are
applied to the prepayment and default functions reported by Model 3 in table 6 to compute the
monthly prepayment and default risks associated with hypothetical 0.5 million RMB mortgage.
We compare two hypothetical mortgage pools characterized by two risk structures between spot
versus forward market mortgage borrowers. The present values of the cash flows from the two
groups allow us to calculate risk premium on the forward presale housing market. 10 Table 8
reports a simulated result on forward risk premium which is about 250 basis points per year. In
other worlds, there is a 2.5% risk premium on forward market relative to the spot market in China.
[Insert Table 8]
6. CONCLUSION
This paper is the first to realize the mortgage risks on forward presale housing market.
This finding indicates that borrower characteristics and collateral information are both important
to determine the mortgage termination risks. Currently most Chinese banks price the consumerloan based on borrower characteristics only. The results of this paper indicate a potential
improvement in banks mortgage risk modeling. In addition, the mortgage borrowers
prepayment and default behavior in the forward housing market is significantly different from
those in the spot housing market. The study found that the cross-subsidy between the forward and
10This is similar to Deng and Gabirel (2006).
8/3/2019 030 - Paper
28/45
26
spot housing market in China can be as high as 250 basis points. The finding of this study will
provide valuable insight about emerging housing and mortgage markets in China as well as those
in other transition economy.
8/3/2019 030 - Paper
29/45
27
Figure 1. Residential Mortgage Market in China
Residential Mortgage Market in China
( 98% AAGR since 1997)
19 43136
338
560
825
1,330
1,592
2,000
0.39%
1.07%
2.14%
5.07%
6.94%
8.59%
9.27%
11.27%
12.00%
0
500
1000
1500
2000
2500
1997 1998 1999 2000 2001 2002 2003 2004 2005
Year
BillionRMBYuan
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
Total Mortgage Outstanding Ratio of Mortgage to Total Bank Loans
Source: Chinese Banking Regulation Committee.
Figure 2. International Comparison of Mortgage to Consumer Loan Ratio
International Comparison of Consumer Loans (2003)
9.1%
26.3%29.5%
34.3%27.3%
38.8%
22.6%
59.2%2.7%
3.3%
2.6%
1.3%
2.4%
2.5%
3.9%
3.7%
3.7%
6.7%4.9%
16.0%
8.7%
28.4%
12.0%
7.5%
0.0%
2.0%1.4%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
China Thailand Malaysia Taiwan HongKong Singapore U.S. Korea U.K.
PercentageofTotalLoans
mortgage credit-card loan other consumer loan
Source: Goldman Sachs
8/3/2019 030 - Paper
30/45
28
Figure 3. International Comparison of Loan to GDP Ratio
International Comparison of Loan-GDP Ratio (2003)
11.4%
19.2%
26.1%
36.6% 34.7%
25.5%
50.0%
57.5%
3.4%
2.7%
4.0%1.5%
3.0%
4.0%
3.6%
3.0%
4.3%
3.7%
6.3%20.3%
32.6%
7.1%
11.7%
7.2%1.6%
0.0%
2.1%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
Thailand China U.S. Malaysia Taiwan Singapore Korea HongKong U.K.
PercentageofGDP
mortgage credit-card loan other consumer loan
Source: Goldman Sachs
Figure 4. International Comparison of Mortgage to Income Ratio
International Comparison of Mortgage-Income Ratio (2002)
7%
17%
30%
55%
75%
89%94%
114%123% 123%
174%
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
India Thailand China Taiwan Malaysia HongKong U.S. Korea Japan U.K. Singapore
PercentageofDisposableIncome
Source: Goldman Sachs
8/3/2019 030 - Paper
31/45
29
Figure 5. Supply and Sales in the Residential Housing Market in China
Supply and Sales of Residential Housing in China
1.58
1.31 1.361.25 1.22 1.2
1.131.03
0
50
100
150
200
250
300
350
400
1997 1998 1999 2000 2001 2002 2003 2004
Year
MillionSquareMeters
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Housing Square Meters Completed Housing Square Meters Sold
Supply-Sales Ratio of Residential Housing
Source: Goldman Sachs
8/3/2019 030 - Paper
32/45
30
Figure 6. Market Microstructure of Forward and Spot Housing Market in China
SimpleModelfor
Forwardv.s.SpotHousingM
arketinChina
1.Forward
HousingMarket
TimeLine
Customer
Developer
Bank
2.SpotHousingMarket
TimeLine
Customer
Developer
Bank
1.ReceiveLastMortgagePayment
1.ReceiveH
ousePriceinFull
2.Depositin
Bank
1.Mortgage
LendingBasedonBorrower
Characteristics
2.TakeDep
ositfromDeveloper
1.New
ARMRateAnnounced
2.PrepaymentRisk,ReceivePayment
atPar
3.ReceiveResidualValueofHousein
CaseofBorrowerDefault
4.ReceiveMortgagePaymentif
OptionnotExercised
T=3
MortgageMatu
rity
1.Purchase
HouseonSpotMarket
2.PayinfulltoDeveloperwith
Downpayme
nt+Mortgage
3.Consume
Housing
1.PrepayifFinan
cing
Cost>Investment
Return
2.DefaultifValue
ofHouseInvestment
Return
2.DefaultifValue
ofHouse= 30 55 3665 38875 42595
(0.13) (8.60) (91.27) (49.78)
Registered Equity
1268 2872 32497 36637
(3.46) (7.84) (88.70) (42.78)
57 4140 44805 49002
(0.12) (8.45) (91.44) (57.22)
Number of ProjectsSingle Property 1373 6592 57495 65460
(2.10) (10.07) (87.83) (63.42)
Multiple Properties 11 3417 34335 37763
(0.03) (9.05) (90.92) (36.58)
Equity < 30 Million RMB
Equity >=31 Million RMB
Table 4. Descriptive Statistics for Mortgage Loans
Frequency of Loans by Category and by Payoff Types(Continued)
(Currency Exchange adj. )
8/3/2019 030 - Paper
38/45
36
Variable Defaulted Prepaid Other All Loans
Marital Status
Married 562 4277 41440 46279
(1.21) (9.24) (89.54) (44.73)
Single 822 5778 50583 57183
(1.44) (10.10) (88.46) (55.27)
Education
College 843 6432 57563 64838
(1.30) (9.92) (88.78) (62.67)
Secondary Sch. 482 3254 31195 34931
(1.38) (9.32) (89.30) (33.76)
Primary Sch. 59 369 3265 3693
(1.60) (9.99) (88.41) (3.57)
Age Cohort
Age < 40 1036 6574 72420 80030
(1.29) (8.21) (90.49) (77.35)
Age > 40 348 3481 19603 23432
(1.49) (14.86) (83.66) (22.65)
Income GroupsMont y Income
< 8888RMB 1006 6623 69403 77032
(1.31) (8.60) (90.10) (74.45)Monthly Income
>8888RMB 378 3432 22620 26430
(1.43) (12.99) (85.58) (25.55)
OccupationBusiness/Trade 248 1854 20303 22405
(1.11) (8.27) (90.62) (21.66)
Social Service 130 849 8759 9738
(1.33) (8.72) (89.95) (9.41)
Self-Employment 602 4960 36746 42308
(1.42) (11.72) (86.85) (40.89)
R&D 80 773 9038 9891
(0.81) (7.82) (91.38) (9.56)
Others 324 1619 17177 19120
(1.69) (8.47) (89.84) (18.48)
Job PositionManager 768 6184 55766 62718
(1.22) (9.86) (88.92) (60.62)
Others 214 607 5457 6278
(10.77) (16.76) (172.48) (6.07)
Technician 168 1256 12482 13906
(1.21) (9.03) (89.76) (13.44)
Clerk 234 2008 18318 20560
(1.14) (9.77) (89.10) (19.87)
Table 5. Descriptive Statistics for Mortgage Loans
Frequency of Loans by Borrower Category and by Payoff Types
8/3/2019 030 - Paper
39/45
37
Default Prepay Default Prepay Default Prepay
Fraction of Contract -2.616 2.722 -3.017 4.618Value (Call Option) (11.93) (30.49) (5.80) (21.45)
Probability of Negative 3.967 2.105 3.533 5.377
Equity (Put Option) (5.69) (13.13) (9.55) (10.04)
Presale 1.058 1.118 1.013 1.097 1.090 1.020
(dummy) (2.56) (28.10) (1.96) (27.56) (2.88) (12.74)
Interaction of Presale -1.937 -2.029
and Call Option (7.42) (8.86)
Interaction of Presale -3.103 -3.462
and Put Option (7.54) (6.45)
age > 40 -0.283 0.105 -0.280 0.111 -0.245 0.103
(dummy) (4.65) (4.73) (4.54) (4.96) (3.93) (4.61)
female -0.044 0.009 0.010 0.020 0.007 0.022
(dummy) (0.82) (0.44) (0.18) (1.02) (0.13) (1.12)
married -0.017 -0.057 -0.027 -0.064 -0.058 -0.067
(dummy) (1.29) (2.85) (1.42) (3.15) (1.97) (3.28)
occupation: -0.077 0.051 -0.095 0.050 -0.022 0.045
business and trade (dummy) (0.84) (1.96) (1.03) (2.33) (0.24) (1.94)
occupation: 0.070 0.013 0.943 0.018 0.054 0.013
social service (dummy) (0.70) (2.33) (0.44) (1.95) (0.53) (0.33)
occupation: -0.141 0.060 -0.180 0.047 -0.106 0.045
others (dummy) (1.78) (2.15) (0.23) (2.62) (1.32) (1.61)
occupation: 0.017 -0.033 0.040 -0.024 -0.136 -0.022
R&D (dummy) (0.15) (2.84) (0.34) (2.17) (1.15) 2.06
education: -0.102 -0.083 -0.110 -0.046 -0.056 0.044
secondary school (dummy) (0.78) (1.55) (0.83) (0.86) (0.42) (0.82)
education: -0.149 0.119 -0.158 0.108 -0.127 0.106
college (dummy) (2.63) (5.37) (2.78) (4.86) (2.23) (4.79)
job position: -0.021 0.045 -0.019 0.036 -0.025 0.036
manager (dummy) (0.24) (2.71) (0.22) (2.18) (0.29) (2.36)
job position: 0.994 -0.042 0.943 -0.041 0.836 -0.040
self-employment (dummy) (1.29) (1.92) (0.85) (2.82) (1.58) (1.88)
job position: 0.013 -0.063 0.031 -0.049 0.082 -0.051
technician (dummy) (0.12) (1.98) (0.29) (1.95) (1.76) (1.45)
number of dependents 0.229 -0.568 0.224 -0.550 0.213 -0.549(20.63) (50.02) (20.09) (48.49) (18.67) (48.40)
log monthly income -0.100 0.130 -0.103 0.123 -0.152 0.122
(2.60) (6.62) (1.63) (6.07) (2.40) (6.03)
Model 1 Model 2 Model 3
Table 6 Maximum Likelihood Estimates for Competing Risks
of Chinese Adjustable Rate Mortgage Prepayment and Default
8/3/2019 030 - Paper
40/45
38
multiple project -1.829 0.077 -1.748 0.119 -1.868 0.116
(dummy) (10.68) (3.35) (10.08) (5.14) (2.40) (5.03)
size -0.104 0.000 -0.099 0.000 -0.099 0.000
(in 10mill. currency adj.) (6.31) (0.79) (5.96) (0.31) (6.44) (0.51)
number of employee -0.063 0.000 -0.060 0.000 -0.061 0.000(15.82) (1.58) (15.25) (1.43) (15.37) (1.00)
license longer than 20y -0.458 0.152 -0.426 0.105 -0.502 0.103
(dummy) (3.86) (6.89) (3.57) (4.72) (4.15) (4.64)
new developer 2.431 0.123 2.499 0.117 2.457 0.118
(dummy) (9.80) (5.13) (9.83) (4.89) (9.57) (4.94)
developer type: joint venture -0.936 0.056 -0.987 0.130 -0.934 0.128
with foreign developer (dummy) (7.16) (1.14) (7.37) (2.68) (6.96) (2.63)
developer type: joint venture 0.834 -0.059 0.844 -0.049 0.800 -0.039
with HK Macau, TW (dummy) (8.59) (0.87) (8.63) (0.72) (8.20) (0.58)
developer type: 0.196 0.158 0.295 0.157 0.299 0.150
private developer (dummy) (1.14) (2.68) (1.72) (2.66) (1.78) (2.55)
developer type 0.504 0.094 0.451 0.101 0.506 0.105
limited co.(dummy) (5.03) (2.36) (4.48) 2.56 (4.99) (2.65)
district 0.399 0.113 0.352 0.108 0.402 0.110
(6.24) 5.05 (5.45) (4.83) (6.17) (4.93)
central city location -1.306 0.086 -1.224 0.084 -1.271 0.085
(dummy) (9.55) (3.38) (8.93) (3.30) (9.18) (3.35)
ratio of certified professionals -4.501 0.256 -4.402 0.269 -4.470 0.271
(9.55) (5.38) (18.38) (5.67) (18.51) (5.71)
Loan To Value Ratio 0.068 -0.043 0.046 -0.073 -0.003 -0.074
(1.70) (3.25) (3.08) (4.11) (0.06) (4.12)
Housing Exp. To Income 0.578 -0.363 0.537 -0.352 0.360 -0.343
(9.95) (12.68) (9.08) (12.43) (5.89) (12.13)
log loan amount 0.129 -0.117 0.047 -0.190 -0.061 -0.191
(0.99) (1.87) (0.72) (1.36) (0.92) (1.53)
stock market 0.002 -0.005 0.002 -0.005 0.002 -0.005
(1.79) (39.45) (0.50) (39.50) (1.43) (39.36)
slope term structure -0.494 -1.549 -0.762 -1.512 -0.649 -1.511
(2.16) (48.74) (3.11) (47.30) (2.65) (47.28)
unemployment 0.059 0.081 0.046 0.077 0.053 0.076
(7.69) (48.20) (5.44) (46.21) (6.27) (46.01)
Log Likelihood
SBC
164107
164638
165089
165545
164254
164747
8/3/2019 030 - Paper
41/45
39
Default Prepay Default Prepay
Fraction of Contract -0.278 4.048 -2.456 2.669
Value (Call Option) (1.45) (9.98) (9.52) (28.76)
Probability of Negative 9.064 2.781 2.762 2.075
Equity (Put Option) (2.35) (2.05) (0.88) (0.56)
age > 40 -0.454 0.127 -0.198