Further Research On Two Exotic Option Pricing Formulas

In this paper,the pricing problem of chooser option and compound option is further studied.Firstly,this paper uses fractional Brownian motion to describe real financial asset prices with the higher peak and fat tail phenomenon,long — term memory and self — similarity characteristic.At the same time,considering the impact of mean recovery of market interest rate on financial market,we use Vasicek stochastic interest rate model to describe the random fluctuation phenomenon of interest rate.Thus,the mathematical model of financial market under fractional Vasicek stochastic interest rate is established.Under this model,the pricing formulas of European simple chooser option and complex chooser option are further discussed by using the risk—neutral pricing method.Finally,the numerical analysis shows that the results are more practical and have some guiding value.Then,in order to describe the non—stationary increment of financial assets,this paper uses bi — fractional Brownian motion,which is more general than fractional Brownian motion,to describe its change,and establishes the corresponding mathematical model of financial market.We studies the pricing problem of compound option by using actuarial approach,when the underlying asset price is subject to bi—fractional Brownian motion,volatility is constant,risk—free interest rate and expected rate of return are deterministic functions of time.The sensitivity analysis of various factors affecting option prices is carried out.The results show that the sensitivity of compound option prices to various factor is closely related to the HK coefficient.