Pricing Of Asian Options Based On Time-Changed Process

Option trading is an important trading method in the capital market,in order to meet the different needs of investors,a variety of new options have emerged.As the most commonly used path-dependent option,Asian options consider the price fluctuation path of the underlying asset,thereby reducing the risk of price manipulation at maturity.As the premiums of Asian options are lower than that of European options,Asian options are favored by investors.Asian option pricing is also an issue of interest to many scholars.In this thesis,we firstly introduce a stochastic process T_α（t） similar to the renewal process to characterize the constant periodicity of financial asset prices in emerging financial markets,secondly,we introduce a mixed Brownian-fractional Brownian motion to describe the peak,thick tail,long-term correlation,and autocorrelation of financial asset prices,finally,a time-changed mixed Brownian-fractional Brownian motion M_α,H（t）=a B（T_α（t））+b B_H（T_α（t）） is constructed.The linear combination of the Brownian motion model and the fractional Brownian motion model is called a mixed Brownian-fractional Brownian motion model,when the Hurst index meets certain conditions,the model is used to price options without arbitrage.This thesis studies the geometric average Asian option pricing based on the time-changed mixed Brownian-fractional Brownian motion.This thesis assumes that the stock price follows a time-changed mixed Brownian-fractional Brownian motion,under the conditions that the interest rate is constant and the interest rate follows the Vasicek interest rate model,using the hedging principle and the non-arbitrage principle,we obtain the partial differential equation that the price of Asian option satisfies,and obtain the pricing formulas for Asian call and put options,as well as the corresponding parity formulas,we have calculated explicit solutions for both cases.