| As an important tool of financial derivatives,options are widely used in risk hedging and management,and are deeply loved by investors.With the rapid development of the financial market,many financial institutions continue to innovate options and design various new options to meet the needs of different investors Because the return of option depends on the change behavior of the price of the underlying asset,and the price of the underlying asset is affected by many uncertain factors in the financial market,the pricing models and methods are different,and the role of risk management is also different.Therefore,option pricing has become one of the important challenges in financial academia.Obviously,in the complex development of market economy,a single option can not keep up with the pace of market development,and the research on new financial derivatives has become the mainstream of academic circles.Asian barrier option is a new type of financial derivatives.Its return depends on the average price of the underlying asset and the barrier value of the barrier asset within the validity period of the option.It covers the advantages of Asian option and barrier option,that is,it avoids that the return of traditional option contract depends on the price of the underlying asset at the time of maturity,and can reduce the risk of investors to a certain extent.However,the barrier assets of standard Asian barrier options are characterized by the underlying assets,which makes it easy for option contract issuers and holders to operate the market or make investment bets.In order to solve these problems,it is very important to describe barrier assets with non-standard assets.Export oriented Asian barrier option is to trigger the barrier level by the change of another asset price related to the underlying asset,and the return of the option depends on the underlying asset.Expanding the inward Asian barrier option of single asset to the outward Asian barrier option of two assets,the pricing result is more conducive to investors’ risk management and hedging.Under Cox,Ingersoll,Ross（CIR）stochastic interest rate,this paper considers the pricing of export-oriented Asian barrier options when the underlying asset price satisfies the time dispersion of stochastic volatility model.Because there are many kinds of Asian options and barrier options,the pricing of option group products is given and numerically simulated in this paper.In terms of mathematical methods,using the methods of stochastic analysis such as Ito formula,Feynman KAC theorem and Fourier transform,the multi-point joint characteristic function required for option pricing is derived,and the pricing analytical formula of this kind of option group products is solved combined with Shephard theorem.In numerical simulation,Monte Carlo simulation method and Multidimensional Discrete fast Fourier transform（FFT）are used to calculate the pricing formula,compare the difference of option price between the two methods,and compare the option price of outward Asian barrier with that of inward Asian barrier,as well as the change of option price of outward Asian barrier under different market models,The sensitivity of correlation coefficient and volatility factors to the price of outward Asian barrier options is further analyzed.The results show that the option price is very sensitive to the asset correlation coefficient,but it is more sensitive to asset volatility,and the volatility of underlying assets and barrier assets have a positive impact on option price,while the volatility of barrier assets has a negative impact on option price.Therefore,investors mainly consider the fluctuation risk of assets when hedging financial investments in line with such option group products,and pay attention to the change of barrier asset price,so as to better control the risk.This paper can be used as a reference for the further study of other qualitative barrier option pricing problems. |
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