Option Pricing Based On The Minimal K-entropy Equivalent Martingale Measure

The options have become the most dynamic financial derivative products as the development of financial derivatives market,so it goes without saying the importance of options pricing.This paper uses a pure jump stochastic process called the finite state multi-period models to describe the dynamics of underlying asset price.Option pricing model for only one underlying asset is considered and the minimum k-entropy equivalent mart-ingale is deduced.On this basis,a pricing method for European option using Monte Carlo simulation named as the minimum k-entropy equivalent martingale pricing method is proposed.Firstly,the feasibility of the minimum k-entropy equivalent martingale measure pricing method is analyzed theoretically.Secondly the minimum k-entropy equivalent martingale measure pricing method with the minimum entropy equivalent martingale measure pricing method and other pricing methods such as Black-Scholes formula are used to evaluate European option price in a virtual Black-Scholes world and the option price of McDonald's stock in the real financial market The comparison reasults verify the feasibility of the minimum k-entropy equivalent martingale measure pricing method.At last,this paperdiscussed the relationship between the market trend of stock price with the relative size of red interest rate and risk-free interest rate under the minimum k-entropy equivalent martingale measure.