Lookback Option Pricing Under CEV Jump-diffusion Process

The Black-Scholes model is a classic option pricing model based on a series of strict assumptions.Since the model was established,the academic community has conducted in-depth research on it.The Black-Scholes model assumed that the volatility of financial asset prices was constant,and empirical analysis showed that the volatility of financial assets was not constant.There is a "volatility smile" phenomenon.The "volatility smile" is caused by the negative correlation between the underlying asset price and the volatility of the yield.The CEV model was used to characterize the correlation between the underlying asset price and the rate of return fluctuations,and at the same time the impact of the jump phenomenon on the underlying asset price was considered.The lookback option pricing was studied in both theoretical and empirical aspects in this article.The main results are as follows:(1)When the underlying asset price was driven by the CEV jump-diffusion process,firstly a portfolio was constructed to replicate the option value,and the no-arbitrage principle was used to establish an integral differential equation model for lookback put option pricing.Secondly Taylor’s expansion was used to expand the integral term in the model into a function on the distribution of stock prices and jump amplitudes to obtain a pricing approximation model,and the partial differential equation model of the lookback put option pricing was obtained.Thirdly we used the progressive evolution method to obtain the lookback option pricing formula under the approximate model,and proved the convergence of the pricing formula.Finally we used numerical experiment compared the value of lookback options under different models.The experimental data showed that the first-order approximation of progressive development was a good approximation of the option value under the CEV jump-diffusion model.At the same time,the effects of volatility,jump strength,and progressive development parameters on the value of options were studied.(2)The pricing of European lookback call options with fixed transaction costs under the CEV jump-diffusion model was studied.Revising the volatility based on the lookback option pricing model under the CEV jump-diffusion model,we obtained an approximate pricing model.The fourth-order Lagrange interpolation polynomial was used to extend the boundary.Numerical experiments showed that the transaction costs ratio increased,the value of options would decreased.(3)The SH50 ETF data,copper futures options data and gold futures options data were used to conduct an empirical analysis on the pricing problem of the CEV jump-diffusion model.The pricing formula for European standard put options under the CEV jump-diffusion model was derived.The SH50 ETF option data,copper option data and gold option data were compared with theoretical values under the Black-Scholes model,Merton jump-diffusion model,and CEV jump-diffusion model.The results showed that the pricing results under CEV jump-diffusion model were closest to the real price.This dissertation totally includes 17 figures,4 table and 86 references.