Dynamic Approach for Index Option Pricing Using Different Models

Option pricing is one of the exigent and elementary problems of computational finance. Our aims to determine the nifty index option price through different valuation technique. In this paper, we illustrate the techniques for pricing of options and extracting information from option prices. We also describe various ways in which this information has been used in a number of applications. When dealing with options, we inevitably encounter the Black-Scholes-Merton option pricing formula, which has revolutionized the way in which options are priced in modern time. Black and Scholes (1973) and Merton (1973) on pricing European style options assumes that stock price follows a geometric Brownian motion, which implies that the terminal stock price has a lognormal distribution. Through hedging arguments, BSM shows that the terminal stock price distribution needed for pricing option can be stated without reference to the preference parameter and to the growth rate of the stock. This is now known as the risk-neutral approach to option pricing. The terminal stock price distribution, for the purpose of pricing options, is now known as the state-price density or the risk-neutral density in contrast to the actual stock price distribution, which is sometimes referred to as the physical, objective, or historical distribution.