Final Draft

Project Report

1Summer Internship Report, SIBM Bangalore

Analysis of options pricing: An Application of BlackScholesModel

Project Report submitted to Symbiosis Institute of Business Management, Bengaluru in partial fulfilment of the course Summer Internship Programme for the award of the degree of Master of Business Administration

Submitted By

Students Name: Sandeep AgrahariPRN: 12020841095

Under the guidance of(Prof Dr Bipasha Maity)

SYMBIOSIS INSTITUTE OF BUSINESS MANAGEMENT, BENGALURU95/1 & 95/2, Electronic City Phase-1, Hosur Road, Bengaluru 560100

Certificate

This is to certify that Mr. Sandeep Agrahari of MBA, 2012-14 Batch, of Symbiosis Institute of Business Management at Bengaluru has done the project entitled Analysis of options pricing: An Application of BlackScholes Model under my guidance.

Name: Mr. Ravi KumarDesignation: Assistant professorDate: 1/07/2013

DECLARATION

I hereby declare that the project work submitted by me entitled Analysis of options pricing: An Application of BlackScholes Model done during my Summer Internship Program (SIP) is submitted as a partial fulfillment of the requirement of MBA program at Symbiosis Institute of Business Management, Bengaluru.

I also declare that this project has not been submitted nor shall it be submitted in future for the award of any other degree or diploma in part or full to any other institution or university.

Place: Bangalore Name : Sandeep AgrahariDate: 01/07/2013PRN : 12020841095

AcknowledgementI take this opportunity to extend my sincere thanks to Mr. Vipin P. Varghese, Regional Coordinator, DBFS for offering a unique platform to earn exposure and garner knowledge in the field of Trading and Market Analysis. During the entire project, I am able to say with conviction that I have immensely benefited from auspicious and prestigious association as a summer intern with Doha Brokerage and Financial Services . I wish to express my deep gratitude to Prof Dr Bipasha Maity, Faculty SIBM who helped me in various ways during our project work. I also would like to thank Professor Ravi Kumar, Faculty Mentor who guided me regarding this project throughout the project work.There are many who I may have left out in acknowledgement, but whose co-operation was indispensable in the fulfilment of the project.

Sandeep AgrahariPRN No 12020841095SIBM Bangalore 2012-2014

Table of ContentsTable of Contents of graphs/tables:6Industry Analysis7Key Features of the Industry7Major Players8Five Years Trend10Company Analysis11Mission11Vision11Organization Structure11HR Details No. of employees13Product and Services13Customers14Competitors14Basic financial Analysis15Operational Processes17Introduction of the Project18Objectives of the study19Literature Review:19Hypothesis Development21Research Methodology:21Data:21Data Type:21Data Source21Data Tenure:21Analysis Tools:22Black-Scholes Formula:22Chi Square formula22ANOVA (ANalysis Of VAriance):23Method :23Limitations of the study24Analysis of Data:25Calculation of Call Price and Variation:25Sector: Bank25Sector: IT29Sector: Pharmaceuticals33Analysis of Companies within the Industry:37Sector: Banks37Sector: IT38Sector: Pharma39Findings and Conclusions40Suggestions41Bibliography42Annexure:43

Table of Contents of graphs/tables:

Sr. No.Table No.DescriptionPage No.

1G-1.1Market share of major brokerage firm9

2T-1.1Details of major players9

3T-2.1Financial Analysis of DBFS16

4T-2.2Financial Ratios of DBFS17

5T-2.3List of Selected companies18

6G-9.1Option Traded quantity of call option of Axis Bank25

7G-9.2Option Traded quantity of call option of ICICI Bank26

8G-9.3Option Traded quantity of call option of HDFC Bank27

9G-9.4Option Traded quantity of call option of KOTAK Bank28

10G-9.5Option Traded quantity of call option of HCL29

11G-9.6Option Traded quantity of call option of Infosys30

12G-9.7Option Traded quantity of call option of TCS31

13G-9.8Option Traded quantity of call option of Wipro32

14G-9.9Option Traded quantity of call option of Dr.Reddy33

15G-9.10Option Traded quantity of call option of Cipla34

16G-9.11Option Traded quantity of call option of SunPharma35

17G-9.12Option Traded quantity of call option of Lupin36

18T-9.1Anova table For banks37

19G-9.13Movement of difference in calculated and actual value on different date for each bank comapny37

20T-9.2Anova Table for ITs 38

21G-9.14Movement of difference in calculated and actual value on different date for each IT company38

22T-9.3Anova Table for Pharmaceuticals39

23G-9.15Movement of difference in calculated and actual value on different date for each Pharma company39

Industry Analysis

The Indian broking industry has evolved in a rapid speed in the last decade and has undergone a significant paradigm shift. This industry has shown most of the negative trapping but now is being considered as a preferred sector for careers irrespective of disciplines. This industry majorly depends upon the number of participants in Stock market, traded volume, and the type of fluctuations. Growing participation by investors spread beyond the traditional geographical pockets, coupled with professionalization of work cultures and demand for value-added services like investment advisory and portfolio management, has created a huge demand for talent at all levels.From the ancient times, Bank sector has always dominated on Indian financial services. However, globalization & liberalization of Indian Equity Markets has led to rapid modernization and the professionalization of the financial sector. In addition, this led to the emergence of the broking industry, as core and important part of financial services sector, competing for talent with banks, insurance companies. The Indian Broking industry is now attracting more of the foreign investors to hedge and maintain their assets and funds. This industry is not only attracting the big players to invest but also small players who want to make good return but with risk.The Indian broking industry is characterized by a huge number of companies ,private or unorganized, now a days. This industry is a fragmented industry with a large number of participants. The industry thus has monopolistic competition a large number of firms selling a slightly differentiated product. Although there are more than 9000 brokers registered with SEBI 80% of the turnover in NSE and BSE is accounted by about 100 brokersThe total trading volume of the Indian brokerage companies stood at US$ 1239.1 billion in the year 2004, which increased to US$ 1492.1 billion in 2005. It is further expected to reach US$ 6535.7 billion by the year 2015.

Key Features of the IndustryStock market development in India was that that it was entirely driven by local enterprise, and later on, many big companies found the opportunity and invested in this sector. Many a factor makes this Industry lucrative.

Low Barriers to entry: In pre-2008, there was a very few formalities to open a brokerage firm but now a days this has certain level of entry barriers. It requires having a certain scale and size as the business involves a high level of fixed costs in the form of technology platform, distribution network and back office operations. In addition, brand recognition is also important to attract new customers.

A commission-based remuneration structure:Brokerage firm earn money through payment of commissions. In this industry , broking firm will earn money on each transaction, irrespective of clients profit/loss status. This industry is sort of risk free industry where the company will make profit, either the market goes up or goes down.

Bargaining power of customer:Many retail investors often lack the knowledge and expertise in the financial sector that calls them to approach the broking houses. The low Product differentiation proves beneficial for the customers. The retail broking services provided by the various companies is homogeneous with very low product differentiation. This allows customers to enjoy a greater bargaining power.

Online Trading System:Almost all the brokerage firms are now providing online features to their clients. It has been the essential feature of any brokerage firm that how smoothly they are providing the technical facility. Many smaller brokerage firms have taken control of most individual investors accounts. They are continuously adding convenience and personal attention to the small investor.

Full-Service and Discount Commissions:The traditional brokerage firms are working on Full-Service commission base service. They have good experience about the market that is why they provide good tips and information, and against this, the client pays a full service charge. Now the scenario is changing, many a brokers are coming out with discounted commission. They do not provide any tips but the commission charge is far below than full-service charge.

Major PlayersBelow is the list of listed companies in NSE/BSE and their share according to market cap.

Graph G-1.1 (Source: www.moneycontrol.com)

Although, many of the good brokerage companies are not listed and they are working as a private firm. Below is the list of top 13 best and the most popular brokerage firm providing best and reliable services. This list is on the basis of survey of investor and trader of many clients.

NameTerminalsSub BrokersNo of EmployeesNo of Branches

Kotak Securities ltd43209104008350

ShareKhan ltd1700190003910581

Angel Broking ltd5715NA284NA

India Infoline ltd173173NA605

Indiabulls2876NA5873522

Reliance Money242814942037142

Motilal Oswal Securities7923890219363

Geojit BNP Paribas627247343314

Karvy Stock Broking ltdNANANANA

Bonanza OnllineNANANANA

HDFC SecuritiesNANANANA

Anand Rathi Securities Ltd15273204566220

NA:Data not available

Table T- 1.1 Source:(http://www.sharegyaan.com/tips-ideas/top-15-best-most-popular-broking-firms-in-india/)

Five Years Trend

This industry has emerged as an attractive industry in the last decade only. Before it, it was present there but due to the lack of technology and support from government, it did not grow as much fast as it has capability.

India Brokerage Industry- Pre 2000

It was known as Mom and Pop shop only. People invested only in Friends and Relatives Business Company. There was no derivative trading. Low trade volumes. Lack of technology. Settlement was T+15 days.

India Brokerage Industry- 2000-2008 Venture capitalist started investing in Brokerage business Huge investment in technology National presence. Traded volume increased drastically A higher volume of derivatives being traded. Margin funds for the retail client.

Indian Brokerage Industry post 2008 Global risk aversion is unwinding and Confidence levels returning, being reflected in performance of the indices Liquidity and credit flows improving Political stability and India re-rating FII and Domestic Flows resuming

Company AnalysisMissionWe are committed to create and enhance wealth for corporate and retail customers, by delivering cutting-edge financial solutions which suit their specific needs.VisionWe want to remain as the leading, trusted total financial services provider, wherever we operate, by maintaining superior technological and service standards, and by keeping trust and transparency as our core values.Organization Structure The company operates regionally and below is the regions in which it operates. Kerala South Kerala North Bangalore Chennai Mumbai Hyderabad.All above regions have the Regional Manager and the Branch Managers for each branch within that region. There are more than 300 employees in the franchisees, but these franchisees are only associated with DBFS. They are not directly related with the company organization structure. They work like independent small business associate who registered themselves with DBFS to get sub brokerage license. The details of the Organization structure are given on next page.

HR Details No. of employeesIn DBFS, there are employees are 250-300 in entire DBFS in India. The head offices Kochin have 100 employees and all 6 regions have 30-40 employees each. In Our Bangalore (Castle street branch) regional office branch, there are 6 employees and a Regional Manager.

Product and Services

DBFS offers a complete life-cycle of investment solution in Equities, Derivatives, Commodities, IPO, Mutual Funds, Depository Services, and Insurance. In the contemporary world, online internet trading has given an enormous space for a wide range of possibilities. The company is diversified in several types of product and services. Below are some services.

Commodities and Forex Trading in DGCX:

DGCX is an initiative of the Dubai Multi Commodities Centre (DMCC), Financial Technologies (India) Limited and the Multi Commodity Exchange of India Limited (MCX). The Management team of DGCX comprises senior personnel from the commodities, securities and financial services industries bringing a wealth of experience and expertise to ensure the success of DGCX.DBFS offers DGCXAs a trading member of DGCX, Dubai, DBFS Commodities DMCC offers trading in commodities and forex for its customers.

Benefits of Trading on DGCXOur range of futures contracts offers participants of the physical commodities markets, such as producers, manufacturers and end users, with a sophisticated means of hedging their price risk exposure. Such price risk management has previously been unavailable to producers in the Middle East. In addition, DGCX offers trading opportunities to financial communities and investment houses in both the Middle East and around the globe who wish to access the growing asset class of commodity and currency derivatives.

Commodities Futures TradingThe group has membership in all premier commodity exchanges in India, namely NCDEX, NMCE and MCX. The company facilitates futures trading for various agricultural commodities and other commodities including crude oil, gold, silver, rubber, cardamom, pepper etc. which are actively traded.

Depository ParticipantDBFS Securities Ltd. is a Depository Participant with Central Depository Services Ltd. (CDSL). CDSL is one of only two depositories in India for electronic holding of securities. The Company extends depository services to its trading clients as well as non-trading clients. The custodial services include electronic holding of securities, Demat, Remat, pledge, unpledge etc. and market and off-market transfers, transmission, transposition etc.

Mutual Funds & InsuranceDBFS, being a total solutions provider for the varied investment needs of the retail investors, distributes Mutual Fund products of almost all major AMCs. Application Forms of NFOs are available with the branches.DBFS does distribute the Life products of TATA Aig and Non-Life products of Reliance Insurance

Portfolio ManagementDBFL Ltd. is a SEBI registered Portfolio Manager with an excellent track record of performance. The group has a highly professional, experienced and result-oriented research team which analyzes the markets and manages the customers funds accordingly in order to ensure optimum results. DBFS Portfolio Managers consistently out-performs the bench-mark indices.

Trading in EquitiesDBFS has membership in both NSE and BSE, MCX. The group has been permitted to operate in the cash as well as derivative segments of NSE and BSE. Online trading in Cash Market and FAO are available at all the branches. Connectivity is provided at the Branches by way of VPN / Broad Band. The group services both retail and institutional customers.

CustomersDBFS serves mainly individual customers, HUF (Hindu undivided family). It also serves many public listed companies and a few private venture firms.

CompetitorsDBFS is mainly present in South India and here the main competitors of DBFS are: Geojit Securities JRG Securities Hedge Equities Share wealth Securities Cap stocks India Pvt. Ltd

Basic financial Analysis

BALANCE SHEET AS AT MARCH 31, 2012Amount in Rs.

31st March 201231st March 2011

Liabilities

SHAREHOLDERS FUNDS 64,066,389 63,393,608

SHARE APPLICATION MONEY PENDING ALLOTMENT 43,999,985 -

DEFERRED TAX LIABILITIES (NET) 2,872,295 3,363,536

LONG TERM PROVISIONS 447,274 508,708

CURRENT LIABILITIES 164,968,344 156,923,360

Total 276,354,287 224,189,212

Assets

FIXED ASSETS

(i) TANGIBLE ASSETS 16,763,630 16,006,162

(ii) INTANGIBLE ASSETS 47,976,260 43,735,926

CURRENT ASSETS 211,614,397 164,447,124

TOTAL 276,354,287 224,189,212

Profit and Loss account AS AT MARCH 31, 2012 Amount in Rs.

31st March 2012 31st March 2011

IREVENUE FROM OPERATIONS 101,800,499 135,782,195

IIOTHER INCOME 21,724,151 21,773,354

IIITOTAL REVENUE (I + II) 123,524,650 157,555,549

IVTOTAL EXPENSES 122,190,095 144,071,983

PROFIT BEFORE EXCEPTIONAL AND EXTRA ORDINARY ITEMS & TAX (III-IV) 1,334,555 13,483,566

EXCEPTIONAL ITEMS

Current Tax 163,630 2,726,897

Deferred Tax 72,565 1,129,243

Short provision of tax of previous year 989,386

PROFIT FOR THE PERIOD FROM CONTINUING OPERATIONS 108,974 9,627,426

Balance Carried to Balance Sheet 108,974 9,627,426

EARNINGS PER EQUITY SHARE:

Basic 0.02 1.67

Diluted 0.02 1.67

Table T-2.1

Ratios:

RatioValue

Debt-Equity ratio0.0070

Current Ratio1.2800

Net Profit Margin ratio0.0012

Gross Profit Margin ratio0.0130

Asset Turnover ratio0.3700

Return on Equity0.0017

Table 2.2Operational ProcessesOperational process as per the customer point of view that how the whole transaction gets completed. It is described in below steps:

The Customers who are interested in trade, they need to be registered clients of this company. In order to become a registered member, client has to fill a KYC form which is mandatory by (SEBI) After verification the client will be registered as a client of DBFS After registration, client will get a client ID that will be a unique ID and client is now ready to any sort of transaction (i.e. equity, commodity, forex, derivatives etc.) Clients can update their DBFS account by providing cheque, DD or they can do online transfer.

Introduction of the ProjectThe Financial industry has always been a speculative industry. People always try to invest money, which give them higher returns. In the hope of higher returns, they also try to take higher risk. Some of the instrument which used to hedge and invest money is called Derivatives. Financial derivatives are financial instruments whose prices are derived from the prices of other financial instruments. The components are Forwards, Futures, and Swaps. Option is also one of the components in financial derivatives. In the global capital markets of today, derivatives occupy an integral part of the economy, and are virtually driving the world markets with the introduction of derivatives trading in the form of futures and options, the Indian capital market too is witnessing a qualitative change. While option trading is not new in the country, the growth in option trading has been accompanied by a tremendous interest among academics and practitioners in the valuing of option contracts. In this project, our study will be concentrated towards pricing of Options in NSE and specifically with the help of Black Scholes formula. We will discuss here call options for stocks only. three industries i.e. Banks, IT and Pharmaceuticals are selected randomly . The companies from each industry have been picked up from Nifty-Fifty as the maximum market share companies. The analysis was done in the month of April when most of the companys quarterly results were coming out. So there was much fluctuation in the option price. For the strike price, it was set at random basis after seeing the fluctuation in share price of that script.Below companies has been selected based on maximum market share from Nifty-Fifty.

NameSector

Axis Bank Ltd.BANKS

HDFC Bank Ltd.BANKS

ICICI Bank Ltd.BANKS

Kotak MahindraBANKS

HCL Technologies Ltd.COMPUTERS - SOFTWARE

Infosys Technologies Ltd.COMPUTERS - SOFTWARE

Tata Consultancy Services Ltd.COMPUTERS - SOFTWARE

WIPROCOMPUTERS - SOFTWARE

Dr. Reddy's Laboratories Ltd.PHARMACEUTICALS

Cipla Ltd.PHARMACEUTICALS

Sun Pharmaceutical Industries Ltd.PHARMACEUTICALS

LupinPHARMACEUTICALS

Table T-2.3

Objectives of the study a) Application of Black-Scholes formula: To apply Black Schole model to calculate the price of options for the given strike rate and given date. b) Factors affecting the price: What all factors have affected the variation in call price from the calculated one.c) Variation (fluctuation) in option price within the industry: For an industry, calculate whether the price variation is similar for all companies within the industry or not

Literature Review:

Many of the paper have been already published regarding the pricing of options using the Black-Scholes formula. The major problem is always considered as volatility of stock. The stochastic nature of the volatility of most of the financial asset is responsible for much of the difficulty. The early test of Black-Scholes (1973) option pricing model rely upon historical prices for volatility estimates and Latane & rendlemans implied volatility technique has become the standard method of estimation. Later on Beckers (1981) stresses that it is inconsistent to use the Black-Scholes model with a constant variance to obtain estimates of ninstationalry variances.The work conducted by Hull and White (1987) and Johnson and Shanno (1987) has been directed at solving the problem of pricing European calls on assets with stochastic volatilities. Hull and White provide a series solution for the case in which the variance and stock price are uncorrelated, convergence is slow unless the variance of the assets' volatility is relatively small. For more general cases, both Hull and White and Johnson and Shanno rely upon Monte Carlo simulations to estimate option prices. The Monte Carlo method tends to be expensive and is often too time consuming for real-time applications.Before introduction of spreadsheet programs, Cox and Rubinstein (1985) showed how to create a simple 2-D table for easy calculation of Blacl-Scholes European call values. Tom Arnold, Terry and Richard again showed in their paper that option pricing tables described in Cox and Rubinstein still have tremendous pedagogical value.In 2008 letter to Berkshire shareholders, Warren Buffett criticized the Black-Scholes option pricing model arguing that it can produce "absurd" values for long-dated put options. Though Mr. Buffett did not explicitiy say so, a careful analysis of his viewpoint reveals that his criticism boils down to the belief that future nominal stock prices are not well approximated by a lognormal distribution with volatility estimated from historical data. Instead, Mr. Buffett apparently believes that inflationary policies of governments and central banks will limit future declines in nominal stock prices compared with those predicted by a historically estimated lognormal distribution. If Mr. Buffett is correct on this point, the Black-Scholes model will indeed significantly overvalue long-dated put options.Despite their popularity and wide spread use, the model is built on some non-real life assumptions about the market. Some assumptions are described as below:a) Volatility - a measure of how much a stock can be expected to move in the near term - is a constant over time. Volatility can be relatively constant in very short term but it is never constant in longer term. Large price changes tend to be followed by large price changes, and vice versa leading to a property called volatility clustering. Measures of volatilities are negatively correlated with asset price returns, while trading volumes or the number of trades are positively correlated, hence volatility cannot be a constant over time.

b) People cannot consistently predict the direction of the market or an individual stock. It assumes stocks move in a manner referred to as a random walk. Random walk means that at any given moment in time, the price of the underlying stock can go up or down with the same probability. This is usually not true as stock prices are determined by many economic factors that cannot be assigned the same probability in the way they will affect the movement of stock prices.

c) Returns of log normally distributed underlying stock prices are normally distributed. This assumption is reasonable in the real world, though not fitting observed financial data accurately.

d) Interest rates are constant and known, just same like with the volatility. It uses the risk-free rate to represent this constant and known rate. In the real world, there is no such thing as a risk-free rate, but it is possible to use the Indian Government T-Bills 90-day rate since the Indian government is deemed to be credible enough. However, these treasury rates can change in times of increased volatility.

e) The underlying stock does not pay dividends during the option's life. In the real world, most companies pay dividends to their shareholders. The basic Black-Scholes model was later adjusted for dividends, so there is a workaround for this. This assumption relates to the basic Black- Scholes formula. A common way of adjusting the Black-Scholes model for dividends is to subtract the discounted value of a future dividend from the stock price.

f) No commissions and transaction costs. The model assumes that there are no fees for buying and selling options and stocks and no barriers to trading. Usually not true as stock brokers charge rates based on spreads and other criteria.

g) Markets are perfectly liquid and it is possible to purchase or sell any amount of stock or options or their fractions at any given time. This again is not plausible as investors are limited by the amount of money they can invest, policies of their companies and by the wish of sellers to sell. It may not be possible to sell fractions of options as well

Hypothesis DevelopmentH0: There is difference between observed and calculated value of option price.H1: There is difference with Share price and difference between observed and calculated values i.e. The fluctuation (difference between observed and calculated values) has same variation within the industry.Research Methodology:

In this section, information about data, tools used to analyze that data and the methods to interpret those data is mentioned.Data:

Data Type:

Almost all the data used in this project is secondary data. The price of shares is taken from the NSE website. From the same website, prices of call options are also taken for a specific exercise price and expiry date.

Data Source:

The analysis of this project is done at office of Doha Brokerage Financial Services. But the data used for analysis is taken from the NSE website.

Data Tenure:

For the analysis purpose, last one year data of all 12 companies has been taken from NSE. Analysis Tools:

Black-Scholes Formula: The Black-Scholes model is used to calculate the theoretical price of European put and call options, ignoring any dividends paid during the option's lifetime. This model has some limitation as follows:

The options are European and can only be exercised at expiration No dividends are paid out during the life of the option Efficient markets (i.e., market movements cannot be predicted) No commissions The risk-free rate and volatility of the underlying are known and constant Follows a lognormal distribution; that is, returns on the underlying are normally distributed. To apply this formula, Black-Scholes takes following variable into consideration.

Current underlying price Options strike price Time until expiration, expressed as a percent of a year Implied volatility Risk-free interest rates

Chi Square formula: Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result.

The formula for calculating chi-square is:

That is, chi-square is the sum of the squared difference between observed (o) and the expected (e) data (or the deviation, d), divided by the expected data in all possible categories.

Step-by-Step Procedure for Testing Your Hypothesis and Calculating Chi-Square

1. State the hypothesis being tested and the predicted results. 2. Determine the expected numbers for each observational class. Remember to use numbers, not percentages.3. Calculate 2 using the formula. Complete all calculations to three significant digits. Round off your answer to two significant digits.

4. Use the chi-square distribution table to determine significance of the value.

5. State your conclusion in terms of your hypothesis.a) If the p value for the calculated 2 is p > 0.05, accept your hypothesis. b) If the p value for the calculated 2 is p < 0.05, reject your hypothesis, and conclude that some factor other than chance is operating for the deviation to be so great.

ANOVA (ANalysis Of VAriance): This tool performs a simple analysis of variance on data for two or more samples. The analysis provides a test of the hypothesis that each sample is drawn from the same underlying probability distribution against the alternative hypothesis that underlying probability distributions are not the same for all samples.

Method :

The first task in this project is to apply Black Scholes model to calculate the price of options for the given strike rate and given date. After calculating the option price, this price will be compared with actual value of option that was being traded on that day and at last for an industry, we have to calculate whether the price variation is similar for all companies within the industry

Steps: a) The standard deviation of the share price of the company will be calculated in the basis of last year share price fluctuations.b) The risk free interest rate has been taken from RBI.c) Exercise price was selected randomly.d) The call option price was calculated on each day having different spot prices for the same script with Black Scholes formula.e) Get traded call option price for the same script, for same exercise price and of same expiry date from the NSE historical data.f) Find out the absolute difference between calculated and actual call option price.g) Apply Chi square test whether those difference are significant.h) If there is significant difference then mention the factor behind the variations.i) At last apply Anova on taking samples from each company of the same industry and find that whether variation in call price was similar or not.

Limitations of the study

1. The Black Scholes model can be applied when the return of underlying asset is normally distributed.2. There should not be much macroeconomic changes. 3. If there is huge difference in calculated and actual value of option, it is hard to decide which factor affected the variation in price.4. The time period of the study was not sufficient for a comprehensive study.5. The secondary nature of the data has been a constraint for the study.6. Different people may interpret the same analysis in different ways.7. The research could confine only to 12 companies from 3 different industries.

Analysis of Data:Calculation of Call Price and Variation:

Sector: Bank

Axis Bank (NSE: AXISBANK):

Date: 23th April Spot Price: Rs. 1444.80Exercise Price: Rs. 1400 Intrinsic value: Rs. 44.80

Call Price (Calculated)46.3617

Call Price (Actual)51.85

Time value (Calculated)1.561703

Time value (Actual)7.05

From the data table of Axis Bank, Call price (at exercise price: 1400) is varying too much form the expected value in the entire month.

Chi-square Probability = 1.052 % < 5% accept the Hypothesis H0.

Reason: Investors were also expecting good quarter result and because of that the demand of call options was high. All the news was in favour of Axis Company which led to the high rate of call price.

Below table deppicts the no of traded contract in this entire month.

No of ContractsGraph 9.1

ICICI Bank (NSE: ICICIBANK):






From the data table of ICICI Bank, Call price (at exercise price: 1150) is varying too much form the expected value.

Chi-square Probability = 0 % < 5% accept the Hypothesis H0.

Reason: Investors were also expecting good quarter result and because of that the demand of call options was high. All the news was in favour of ICICI Company which led to the high rate of call price.

Below table depicts the no of traded contracts in the entire month.


HDFC Bank (NSE: HDFCBANK):

Date: 23th April Spot Price: Rs. 689Exercise Price: Rs. 650 Intrinsic value: Rs. 39





From the data table of HDFC Bank, Call price (at exercise price: 650) is not varying too much form the expected value for the entire month period.

Chi-square Probability = 18 % > 5% Reject the Hypothesis H0. The variation is only by chance not only due to any factor.



KOTAK Bank (NSE: KOTAKBANK):





Time value (Actual)-0.35

From the data table of KOTAK Bank, Call price (at exercise price: 660) is varying too much form the expected value.

Chi-square Probability = 91 % > 5%

Reject the Hypothesis H0. The variation is only by chance not only due to any factor.



Sector: IT

HCL (NSE: HCLTECH):

Date: 16th April Spot Price: Rs. 762Exercise Price: Rs. 800 Intrinsic value: Rs. 0





From the data table of HCL , Call price (at exercise price: 800) is varying too much form the expected value for few dates.


Reason: Investors were also expecting good quarter result and because of that the demand of call options was high. All the news was in favour of HCL Company which led to the high rate of call price but later on there was reduction in price due to actual quarter result.



INFOSYS (NSE: INFY):

Date: 11th April Spot Price: Rs. 2916.7Exercise Price: Rs. 2950Intrinsic value: Rs. 0





From the data table of INFOSYS, Call price (at exercise price: 2950) is varying too much form the expected value for most of dates.


Reason: The price of infy script was increasing at a very high rate and investors has lot of faith in this company which led to shoot up the call price.



TCS (NSE: TCS):






From the data table of TCS, Call price (at exercise price: 1600) is varying too much form the expected value for all the dates.


Reason: Few of the news before 16th April, actually led to the higher call price and people were expecting good result this time, But later on there was drastic movement in call price and TCS shares fall suddenly which also reflected in call price.



WIPRO (NSE: WIPRO):






From the data table of WIPRO, Call price (at exercise price: 450) was not varying too much but it was deviating more form the expected value for all the dates.


Reason: Investors were very bearish on this stock and very little trade happen for this script. There was no demand for this call option so the price fell down.


No of Contracts

Graph 9.8

Sector: Pharmaceuticals

Dr. Reddy (NSE: DRREDDY):






From the data table of DrREDDY, in 1st week of April the call price (at exercise price: 1900) did not deviate from the expected value but after 1st week there was much difference between expected and calculated value.


Reason: Although the quarter 4 result was going to announce in May but investors were expecting a positive growth in stock of Dr. Reddy.



CIPLA (NSE: CIPLA):

Date: 18th April Spot Price: Rs. 401.15Exercise Price: Rs. 400Intrinsic value: Rs. 1.15





From the data table of CIPLA, the call price (at exercise price: 400) did not deviate from the expected value .

Chi-square Probability = 99 % > 5% Reject the Hypothesis H0. The little bit variation is only due to chance.

Reason: the Q4 result was suppose to come in May and due to very few news regarding Cipla, It did not show fluctuation as other script showed.



SUN PHARMA (NSE: SUNPHARMA):

Date: 15th April Spot Price: Rs. 873Exercise Price: Rs. 900Intrinsic value: Rs. 0





From the data table of Sun Pharma, in 1st and 2nd week the call price (at exercise price: 900) deviated much from the expected value .

Chi-square Probability = 2 % < 5% Accept the Hypothesis H0.

Reason: The Q4 result was about to come in last week of April so some the investors showed interest in this script but after 2nd week investors did not show much interest in this script.



LUPIN (NSE: LUPIN):






From the data table of LUPIN, the call price (at exercise price: 660) did not deviate from the expected value much .

Chi-square Probability = 32 % > 5% Reject the Hypothesis H0. The little bit variation is only due to chance.

Reason: the Q4 result was supposed to come in May and due to very few news regarding LUPIN, It did not show fluctuation as other script showed.



Analysis of Companies within the Industry:

Sector: BanksApplication of One-way Anova to measure the means of each company deviation.

Anova: Single Factor

SUMMARY

GroupsCountSumAverageVariance

AXIS1637.935122.370946.43428

ICICI1622.371871.398241.65361

HDFC1633.238772.077420.79160

KOTAK1615.017910.938621.46350

ANOVA

Source of VariationSSdfMSFP-valueF crit

Between Groups20.2131036.7377012.6057050.0599602.758078

Within Groups155.14497602.585750

Total175.3580763


Table T-9.1

Since F value < F Crit, So Our Hypothesis is correct and we will accept is that there is relation in between fluctuation in difference of observed & calculated and Share price of scripts.

Graph G-9.13Sector: IT

Application of One-way Anova to measure the means of each company deviation.


SUMMARY


HCL1674.57324.660817.2476

Infy16227.202214.2001362.5979

TCS16129.28938.080642.1063

Wipro16-23.2500-1.453111.7552

ANOVA


Between Groups2053.75523684.585056.313800.000862.75808

Within Groups6505.604060108.42673

Total8559.359263


Table T-9.2

Since F value > F Crit, So our hypothesis H1 is wrong and we will reject the hypothesis. So there is no relation in between fluctuation in difference of observed & calculated and Share price of scripts.

Graph G-9.14 Sector: PharmaApplication of One-way Anova to measure the means of each company deviation.


SUMMARY


Dr Reddy1661.431083.8394412.08700

Cipla1610.584110.661510.40212

SunpPharma1630.921541.932602.12653

Lupin1617.246631.077915.77321

ANOVA


Between Groups95.52366331.841226.246790.000922.75808

Within Groups305.83289605.09721

Total401.356663


Table T-9.3

Since F value > F Crit, So our hypothesis H1 is wrong and we will reject the hypothesis. So there is no relation in between fluctuation in difference of observed & calculated and Share price of scripts.

Graph G-9.15Findings and Conclusions

Volatility in Price of Script:

Price volatility plays an important role to the change in price of options. It fluctuates dramatically while changing in script price.

Psychology of Indian Market:

The news played a very significant role while pricing the call price in NSE. Indian traders are very emotional, they extremely believe on news only not the fundamental analysis. The moment any news came there was too much variation in the call price.

Traded Volume of Option Contracts:

The trends showed that no of contracts traded were highest when they were near to expiry date.

Difficult to determine the actual factors behind the variation in prices

No factors can be determined that which led to the change in variation of call price. The major roles were played either by the quarter result of the company or the news or the report from any of the analyst.

Difference between calculated and actual price, varies much from sector to sector.

Suggestions

Time Period of Analysis

The time period of analysis should lie in between July to December. This period is known as stagnant period. During this period RBI is very unlikely to change the interest rate, the annual result of most of the company also did not fall in to this period etc. So no macroeconomic factors play any role in fluctuation of market/ script trend.

Duration of Analysis:

The duration must be at least 4-6 month to get the proper result from the Black-Scholes formula.

Picking up the script for analysis

The Black-Scholes formula is suitable for those scripts of which returns are normally distributed. It is advisable to check the returns of the script before picking for the analysis.

Volatility measurement

The measures of volatilities are negatively correlated with asset price returns , while trading volumes or the number of trades are positively correlated, hence volatility cannot be a constant over time. Some of the advanced option valuation models substitute Black-Scholes's constant volatility with stochastic process generated estimates.

Bibliography

www.nseindia.com

www.dbfsindia.com

www.search.ebscohost.com

www.jstor.org

www.sebi.gov.in

www.teachexcel.com

www.indiaonline.in

www.bseindia.com

Arnold, Tom; Nixon, Terry D.; Shockley, Richard L., Jr.; Journal of Applied Finance, Spring-Summer 2003, v. 13, iss. 1, pp. 46-55.

Cornell, Bradford; Journal of Portfolio Management, Summer 2010, v. 36, iss. 4, pp. 107-11.

Journal of Financial & Quantitative Analysis. Dec89, Vol. 24 Issue 4, p527-532. 6p.

John Adams, Hafiz, Robert and David. Research methods for graduates business and Social Scinces. Response Publication.

Simon Benninga. Financial Modeling (With CDROM). MIT Press (MA) (2008)

Takada, H.H.; de Oliveira Siqueira, J. In: AIP Conference Proceedings, 2008, vol.1073, pp. 332-9, Conference Paper in Journal.

Teneng, Dean; International Research Journal of Finance & Economics, 2011.

Annexure:

6

5

Date post:	15-Nov-2015
Category:	Documents
Upload:	sandycse2005
View:	216 times
Download:	0 times

Final Draft

Documents