Firstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman-Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset price, which exists an affine solution. Then, we employ the fast Fourier Transform (FFT) method to obtain the approximate numerical solution of a power option which is conveniently designed with different risks or prices. Finally, we find the FFT method to compute that our option price has better stability, higher accuracy, and faster speed, compared to Monte Carlo approach.
We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.
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