Research On European Option Pricing Based On Prospect Theory

Black and Scholes model is considered as a milestone in the option pricing literature since 1973,it is widely applied in financial markets.Nevertheless,empirical studies on quoted options highlight deviations from the theoretical model,market anomalies such as volatility smiles can not be explained under the framework of traditional financial theory.For this problem,one does not take individual heterogeneity into consideration is one of the reasons.In 1990 s,behavioral finance,based on the prospect theory,has been developed.According to the prospect theory,individuals do not always take their decisions consistently with the maximization of expected utility,and they have biased probability perceptions.Risk attitude,loss aversion and subjective probability are described by value function and weighting function,which is more real,and can explain market anomalies much better.This paper has done three works based on prospect theory: Firstly,extending Black and Scholes model to a market with transaction cost of options and the underlying stocks,deriving numerical results.From the writer's view,price is much higher which means they wish to transfer the transaction cost to the holders,on the other hand,holder also consider the cost,therefore the price is much lower.Secondly,considering the market in which the price of underlying asset follows jump-diffusion process,deriving pricing equations and numerical simulation solutions for European option.Since the price of the underlying asset has the phenomenon of discontinuously jumping,the pricing result was higher than before,which is consistent with the characteristic of option,higher volatility,higher value.Thirdly,conducting option pricing based on multi-period binomial model,using the real exchanging data of50 ETF to conduct the empirical test,indicating that theoretical result fits real exchanging price well,and the result is much better than the traditional one,calibrating model parameters to market data in order to obtain an estimate of the market sentiment,which shows an aggressive market.