A Quasi-Laplace Distribution Monte Carlo Method In Option Pricing

Options can be used to hedge risks,hedging and gain high returns.The reasonable pricing of options is of great significance to option traders in financial derivatives markets.Black-Scholes model is a classical option pricing model,whose return on underlying assets usually assumes normal distribution,but may not be reasonable in practice.This paper presents a Quasi-Laplace distribution instead of its normal distribution,and then uses Monte Carlo simulation method to price options based on the improved Black-Scholes model.Moreover,the volatility of the return on underlying assets usually assumed in the Black-Scholes model is a fixed constant,but it may not be reasonable in the real world.Therefore,this paper chooses a GARCH(1,1)model for the volatility of the return on underlying assets.Assumed that the estimated value of risk-free interest rate is not a fixed constant,we compare the pricing effect of two Black-Scholes models based on historical volatility and two Black-Scholes models based on volatility predicted by the GARCH(1,1)model on SSE 50 ETF options.The numerical results show that the Quasi-Laplace distribution Black-Scholes model based on volatility predicted by the GARCH(1,1)is the best pricing effect on In-the-money options.The estimated price of At-the-Money and Out-of-the-Money options by the normal distribution Black-Scholes model based on volatility predicted by the GARCH(1,1)is closer to the market real price of options.The first chapter of this paper mainly introduces the elementary theories.In the second chapter,we introduce the normal distribution Black-Scholes model and Quasi-Laplace distribution Black-Scholes model.In the third chapter,the GARCH(1,1)model of the volatility of the return on underlying assets is introduced.In the fourth chapter,the numerical results show the pricing effect of different models on different options.Finally,the conclusions of this paper are summarized.