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Fast Fourier transform based power option pricing with stochastic interest rate, volatility, and jump intensity. (English) Zbl 1397.91569

Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60J75 Jump processes (MSC2010)
65T50 Numerical methods for discrete and fast Fourier transforms
91G60 Numerical methods (including Monte Carlo methods)
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