The world financial market has undergone qualitative changes in the last three decades due to phenomenal growth of derivatives. With the world embracing the derivative trading on a large scale, the Indian market cannot remain aloof, especially after liberalization has set in motion. Derivative trading was introduced in phased manner over a period of time.
Among the derivatives, options and futures contracts have been the most dominating one. However, regarding the hedging of stock, option has been the most effective one. Pricing is the most important part regarding the effectiveness of the option contract. Among the various option-pricing model, Black and Scholes model is the most efficient and globally used pricing model.
As India has already introduced stock option contract and has gained momentum in Indian Financial Market, the study of Black and Scholes option pricing model in Indian context is very important and contextual as well. That's why Black & Scholes option pricing model is the topic of this dissertation.
Albeit no generalization can be made, but Black & Scholes option pricing model reasonably holds good in Indian context. Hence, investors can use Black and Scholes option pricing model to determine the fair pricing and risk aspect of given option which is instrumental to formulate effective option strategies for effecting hedging. But investors should not fully depend on this model only. This model should be taken as a transformation model rather than exact pricing model. Stock price, strike price, maturity period, risk free interest rate and volatility are the key variables in Black & Scholes option pricing model.
[...] The dissertation is the study to find out whether the Black & Scholes option-pricing model is applicable in Indian stock market along with its application for finding out the option price and Greeks symbol like Delta, Gamma, Vega, rho of some Indian companies so that investors will be able to find out the relationship of option price with respect to stock price, interest rate and premium which in turn help them to abstract a clear picture of the future for the given contract STATEMENT OF PROBLEM This dissertation is the analysis of the applicability of Black & Scholes option pricing model in India stock market along with its application to find out the option price of some widely traded Indian companies NEEDS AND IMPORTANCE OF THE STUDY India introduced stock option contract just two years back and has become one of the major part of derivatives for hedging the risk in Indian Financial market. [...]
[...] Similarly, the Black and Scholes formulae are useful to calculate option pricing whereas Kolmogorov –Smirnov test is instrumental to test the normality. This chapter basically deals with the methodology that has been employed in this dissertation. It covers the type of research; sampling technique used in this dissertation, sample size chosen, sample description, data collection, types of hypothesis used and the tools used in the hypothesis. Each will be described separately under the following headings TYPE OF RESEARCH Research design is purely and simply the framework for a study that guides the collection and analysis of data. [...]
[...] For Black and Scholes model, it is calculated by using the following formula Where A high value of Vega suggests that option value is very sensitive to small changes in volatility while a low Vega implies that volatility changes over time cause relatively insignificant impact on the option price Assumption Underlying Black and Scholes Model The Black and Scholes model valuation is based on certain assumptions. They are as follows The option being valued is European style option, with no possibility of an early exercise There no transaction (dealing) costs and there are no taxes The risk free interest rate is known and constant over the life of the option The volatility of the underlying instrument (may be the equity share or the index) is known and constant over the life of the option The distribution of the possible share price (or index levels) at the end of time is log normal or in other words, a share's continuously compounded rate of return follows a normal distribution. [...]
[...] Approximately daily stock prices have been used for each company from July to April to test the applicability of Black and Scholes model. Similarly, option contracts that are to be analyzed have been selected from The Economic Times at different date of the month INSTRUMENTAL TECHNIQUE A key assumption underlying the Black and Scholes formulation is that the distribution of possible share prices (or index levels) at the end of a period is log normal or, in other words, a share's continuously compounded rate of return follows a normal distribution. [...]
[...] D-statistics Name of the Year Histogram company Observed Critical value at significance Application of Black and Scholes model in option pricing CALL EQUITY OPTION OF SATYAM COMPUTER (6TH MARCH ) The details of the given contract are as follows: Stock price = Rs Strike price = Rs Risk free rate of return = Expiration date = 27th March (In India Option is expired Only on the last Thursday of the month) Calculation of Volatility: The volatility of Satyam computer has been calculated below in the table using Microsoft Excel. [...]
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