The Promotion Of Option Pricing Formula

Black and Scholes (1973) first proposed the famous Black-Scholes pricing model on option pricing and gave the explicit expression of European option price. Since then the theory has rapidly developed. With the complex economic environment changing, assumptions of Black-Scholes pricing model become increasingly incompatible with the actual situation.To get more realistic results,some scholars modified the model in interest rates,volatility,dividends,transaction costs and etc, at the same time another scholars tried to find some numerical methods to pricing problem.Also,some scholars researched the evolution law of the original asset and obtained some valuable results.In this thesis we first make a detailed review of option pricing, then we study option pricing and make progress in the following aspects.First,in the second chapter we use a relatively simple method—use two relatively simple two-value option to replicate the value of European options with dividend, in this way we can derive the option(European Call and Put Option) pricing formula with dividend.Second,in the third chapter we describe the Binomial method to get the price for-mula of option with dividend. Also, we introduce the Trinomial modle.Then, we make some exploration on the Binomial model—we assume that the financial environment is random and it is a Markov process. If we know the information of the economy, we get the approximate price of option and we give an example to show the algorithm.Third, in the fourth chapter we apply a semi-Markov process theory to describe the underlying asset(you can make sense it is the generalization of the Binomial method) and study the option pricing under such circumstances. We obtain recursive price for-mulas of the European option(with dividend)and the American option.