An alternative option pricing model is proposed, in which the stock prices follow a diffusion model with square root stochastic volatility and a jump model with log-uniformly distributed jump amplitudes in the stock price process. The stochastic-volatility follows a square-root and mean-reverting diffusion process. Fourier transforms are applied to solve the problem for risk-neutral European option pricing under this compound stochastic-volatility jump-diffusion (SVJD) process. Characteristic formulas and their inverses simplified by integration along better equivalent contours are given. The numerical implementation of pricing formulas is accomplished by both fast Fourier transforms (FFTs) and more highly accurate discrete Fourier transforms (DFTs) for verifying results and for different output
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