BY Ashutosh Roy

IIM Ahmedabad

Convenience Yields Modeling as Call Options: Indian wheat

Market

National Workshop on Commodity Research Organized By NCDEX (NICR)

10th October 2007, India International Centre

Convenience Yield (CY) defined Convenience Yield Defined as “This definition presents

convenience yield as a benefit which accrues to inventory holders from the increased utility associated with availability at periods of scarce supplies”.

A “negative component of carrying charges” in an effort to explain the often observed phenomenon of spot prices being higher than futures prices. [Kaldor (1939); Working (1948, 1949)]

This article examines empirically the behavior and determinants of convenience yield over time for wheat.

As a new approach convenience yields are treated as call options with identifiable exercise price, time to maturity and underlying asset.

CY Explained DimensionConvenience Yield ( CY ) has been addressed

through following approachesConvenience yield is inverse relation with stock

[Brennan (1958); Telser (1958)] [Brennan (1986); Fama and French (1987)]

Time Varying beahaviour beaucse of sypply dynamics (crop related seasonality) Fama and French (1987)

convenience yields as call option value. A holder can hold only in case or CY is greater than storage and risk premium. Heinkel, Howe, and Hughes (1990)

This study conducts an empirical investigation of whether convenience yields have the characteristics of call option.

Crop Cycle – Uncertainty Modeling

)1,0()1,0()0()1,0( VCPF 0)1,()1,()( zCzFzP

V (May, Nov) = V (Dec, May) - V(December, Nov)

CY

Hypothesis Formulation

H1 : Negative relationship between stock and convenience yield ( Theory of storage and Normal Backwardation) [Kaldor– Working–Brennan (1986)].

H2: Since an Option value increases with increase in volatility of price of underlying, the CY will increase as volatility in spot market increases.

H3: Time varying option value; CY by holding the commodity is different at different point in crop cycle.

V (Oct, Dec) < V (Jan, March) < V(May, July). This indicates a type of term structure for convenience yield.

H4: Correlation of intermediate period spot and futures prices will be high when convenience yields are low and vice versa

Data and Computation Hypothesis investigation on wheat futures marketRationale : Availability of monthly stock data Futures Market : Further NCDEX has hosted wheat

futures contract from September 2004 to March 2007.

Total of 32 wheat contract historical prices has been used to estimate the convenience yield.

Spot Price Concern : Spot market co-integration status does not confirm for sanctity “ONE” national price of wheat, because of large geographically spread and several varieties.

Spot market price coming from different markets may not be the good container for spot price information.

To take care of these nuances, near month contract expiry month has been used as indicative spot price.

Convenience Yield Computation

Convenience yield has been estimated here by using the “Cost of Carry Model”, using near month futures prices for calculating the basis (future – spot).

Where ‘r’ is Interest rate ( assumed as 8% per annum) , ‘c’ is Storage Cost ( assumed as 24% per annum including warehouse , insurance , maintenance cost etc.) and ‘y’ is convenience yield.

All parameters r, c, and y have been assumed as proportionate to price of underlying asset.

Data preparation has been done by considering concurrent contracts.

For a given running contract of maturity month ‘M’ which is going to be mature on 20th of month M, if we take another contract which is maturing on 20th of next month M+1, for the common period of trading days we can use contract maturing in month M as spot price and contract M +1’s price as futures price (with one month as time duration).

Since wheat contract has contract period of 6 months, we get six concurrent contracts at any point of time. The near month maturity contract price has been considered as spot market and remaining 5 contracts provide the forward rate for next 5 months.

c-y)t(r ee Spot Pricice Futures Pr

Forward Rate – Computation

1-Mar 2-Apr 3-May 4-Jun 5- Jul 6 -Aug

Mar -Contrac

t

2-Mar 3-Apr 4-May 5-Jun 6- Jul

Apr – F1

Contract

3-Mar 4-Apr 5-May 6-Jun

4-March

5-Apr 6-May

5-March

6-AprMay –

F2Contrac

tJun – F3Contrac

tJul – F4Contrac

tAug – F5

Contract

6-Mar

Current Month – February Spot,

St

3M

2M

1M

4M5M

c-y)t(re PriceSpot Price Futures

On a specific date – Ft ( current month maturity) , as

spot priceMonthly Convenience

Yield

Using the Contract maturing in next month

Using the Contract maturing in next 2 month

Using the Contract maturing in next 3 month

Using the Contract maturing in next 4 month

Using the Contract maturing in next 5 month

tS

t

t

S

Fcr

)1,(ln1

t

t

S

Fcr

)2,(ln*

2

12

t

t

S

Fcr

)3,(ln*

3

13

tS

tFcr

)4,(ln*

4

14

St

Fcr

t )5,(ln*

5

15

Average of five convenience yield obtained as explained above provides a single CY for a

particular day.

Results – H1 ( Negative relationship between stock and convenience yield)

Mean yield

-2

0

2

4

6

8

10

12

Mean

Decreasing Convenience Yield

with Stock levelCY (%)

Wheat Stock Million Tones

Results – H2 : Option value increases with increase in volatility

In H1 we saw negative relationship of CY with stock

Here in this graph, volatility has negative relation ship with stock

Hence CY has +ve association with volatility

Decreasing Price Change

( volatility) as stock increases

Time Varying CY1M – 2M – 3M – 4M Forward Rate

1- Month Forward Rate (CY)

-20%

-15%

-10%

-5%

0%

5%

10%

15%

Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07Time

CY

Flush Period

Lean

2 - Month Forward Rate (CY)

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07

Time

CY

Flush Period

Lean

3- Month Forward Rate (CY)

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07

Time

CY

Flush Period

Lean

4- Month Forward Rate (CY)

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07

Time

CY

Flush Period

Lean

Results – H3 Yield Surface : H3: Time varying option value

Increasing curve at Dec ( because from Dec to May market faces lean period)

Downward Sloping curve at Apr ( because from Apr to Sept market faces lean period)

Month s ( point

of reference)

Forward Rate for

1month to 5

month

CY (

Forw

ard

R

ate

)

Results – H4 ( High Correlation High CY and Vice Versa)

Low CY Zone High CY ZoneHigh CY

Zone

Conclusion and Discussion The empirical results on wheat here give strong

support to theoretical models which view convenience yields as options.

The empirical analysis shows that CY payoff has the characteristics of a call option with stochastic exercise price.

This call option exhibits a type of term-structure which resembles seasonality within the crop cycle

This indicates the potential of Option contracts in the current Indian commodity futures market

Even the options trading is not allowed, the inherent dynamics is observable in the market.

Thank You

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