| A large number of empirical analysis show that depicting stock price morereasonable model should be able to fully consider the influence of some very important onstock price, at the same time,combined with market volatility factors random changes, ect.The double exponential jump diffusion is able to reproduce the leptokurtic feature of thereturn distribution and the volatility smile observed in option price, and also the modelfits stock data better than the normal jump diffusion model, so it is commonly in researchof mathematics and financial. So the model with parameters is more emphasis in theresearch, such as stochastic interest rate, stochastic volatility or stochastic intensity. Thearticle is to add the three parameters in the model at the same time, firstly thecharacteristic function of the proposed model is derived. Monte Carlo simulation is widelyused in study of financial mathematics pricing numerical method, it is used to estimate foroptions. Though its convergence speed has nothing to do with the problem of dimension,it can greatly reduce the computation cost, but the time complexity of this technology isvery high, it need large amount of calculation, so it is rarely used in practice. Recently,FFT has been widely used in the valuation for financial derivatives, because it is fast,accurate, easy to implement.So the FFT application in the financial derivatives pricing isof great theoretical and practical significance. The fast numerical solutions for Europeancall and put options pricing based on characteristic function and fast Fourier transformtechnique are developed. At last，by using fast Fourier transform method and Monte Carlosimulation method to value option price, to compare the fast Fourier transform methodand Monte Carlo simulation method, numerical results prove that the fast Fouriertransform method is considerably accurate, fast, competent and easy to implement. |
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