Research On Option Pricing Based On Time-varying Levy Process And Leverage Effects

It is widely recognized that option is an important derivative for managing risk,the pricing of option is a hot issue in academic circles.And the key to pricing option precisely is to describe the stochastic process governing underlying asset dynamics.Brownian motion has emerged as the benchmark process for describing asset returns in continuous time.But many studies of time series of asset return and derivatives prices finds that it cannot characterize three typical facts of the actual market.First,the jump in asset prices has led to a non-normal return distribution,return distribution are more leptokurtic than the normal distribution.Second,return volatility varies stochastically over time.Third,the negative correlation between asset returns and volatility,that is,the leverage effect.Scholars describe the non-normal characteristics of asset prices and the movement of asset prices by introducing a pure jump Levy process.This paper models the asset price movement process based on the purely jumping Bilateral Gamma process.Considering the discontinuity,time-varying volatility,and leverage effects of actual observed prices,the generalized autoregressive conditional heteroscedasticity(GARCH)is used to model the volatility,so we propose a pricing model that can explain typical facts of asset prices in a discrete framework based on the Bilateral Gamma process and the GARCH-type model.The risk-neutral process of BG-GARCH-type model can be found through a proper measure transformation.This paper uses the maximum likelihood function and generalized moment conditions to estimate model parameters.Under the risk-neutral measure,we price the options using Monte Carlo simulation.The empirical research part of this paper estimates the model parameters by the adjusting closing price of the Shang Hai 50 ETF.The Shang Hai 50 ETF option data are divided into nine categories according to their moneyness and time-to-maturity.By the moneyness,a call option can be classified as out-of-the-money,at-the-money,in-the-money.By the time-to-maturity,an option can be classified as short-term,medium-term,long-term.We compare the pricing accuracy of three models: Black-Scholes model,Normal-GARCH-type model,BG-GARCHtype model,and we show the performance of an option pricing model measured by four statistics: the average absolute error(AAE),average prediction error(APE),average relative pricing error(ARPE),root mean-square error(RMSE).We find that all three models have good pricing results for in-the-money options.Compared with Black-Scholes model and NormalGARCH-type model,the pricing accuracy of BG-GARCH-type model is improved,especially for in-the-money options.As the leverage effect of the SSE 50 ETF market is not significant,the pricing accuracy of the GJR-GARCH model that takes into account asymmetric effects has not significantly improved.