Geometric Average Asian Power Option Pricing Under Jump-fraction Process

Asian power option which combines the advantages of power options and Asian options is a strong path-dependent option.It can avoid the change of financial market caused by price fluctuations.At present,scholars have mostly established the problem of Asian option and power option pricing based on Geometric Brownian motion respectively,and assumed that there is a continuous market without transaction costs.However,in the real financial market,the price changes of the underlying assets present the features of “asymmetric leptokurtic and fat tail” and self-similarity,with the jumping characteristics because of the influence of emergencies,and it also exists transaction costs in the market.Therefore,this paper will study the Asian power option pricing with monotonous transaction costs under the Jump-fraction Process.The main results are as follows:(1)At first,this paper will derive the stochastic partial differential equation satisfied by the Asian power option price according to construct portfolio and jump-fraction ?Ito formula.The analytical expression of the option value is obtained to turn the three-dimensional problems into two-dimensional problems through variable substitution.Finally,the Matlab software is used to numerically simulate the option pricing formula,and discuss the effects of Hurst exponent,jump intensity,power index and expire date on option value.(2)This paper establishes a Asian power option pricing model with monotonous transaction fees and fixed price in accordance with self-financing strategy and jump-fraction formula,and modifies the volatility by defining the leland number,and then solves the model through variable substitution to obtain the Asian power option pricing formula.At last,the Matlab software is used to numerically simulate and calculate the option pricing formula,then discuss the influence of Hurst exponent,jump intensity,power index,trading interval and parameters a,b on option value.(3)It establishes a geometric average Asian power option pricing model with monotonous transaction fees and floating price under the Jump-fraction Process,derives the pricing formula of Asian power call option through variable substitution,Green function and d function.Finally,the Matlab software is used to numerically simulate the option pricing formula,and then discuss the effects of Hurst exponent,jump intensity,power index trading interval and parameters a,b on option value.