Modification And Extension Of Multi Factor Option Pricing Model

In the risk neutral world,Black,Scholes and Merton develop Black-Scholes-Merton model in the field of option pricing.The model provides a theoretical basis for the study of option traders' market operation and future generations' option pricing.Firstly,the thesis briefly introduces the Black-Scholes-Merton model under many restrictions.Under the conditions that the stock price obeys the Generalized Wiener process,the stock does not pay dividends,and the volatility of stock price and the risk-free rate are constant,the option pricing model is derived,and the formula of the European call option is obtained.Secondly,the historical data of the recent stock price is observed,and the current and future volatility and correlation coefficient are estimated from historical data.Since the long time data has less significance for the model,we give the historical data of continuous compound interest rate of different weights.In addition,we also consider the fact that the return rate is negative in the actual situation,and give different weights to different symbols.Thirdly,the thesis considers the influence of the inflation rate on the interest rate,so that the nominal interest rate in the classical model is more close to the real interest rate and inflation rate.Then we modify the Black-Scholes-Merton model,which takes into account the dividend and transaction costs of known dividend rates and transaction rates.Finally,we extend the classical Black-Scholes-Merton model to the option pricing model with the inflation rate and the estimated volatility based on the one-dimensional It?'s lemma and the above mentioned improvements.Furthermore,we derive the multidimensional It? lemma,and construct the investment strategy to extend the option pricing model to the multidimensional form.And we give the analytical formula of two dimensional European call option under limited conditions.