Abstract
In this paper, European option prices are computed analytically, as well as simulated, for underlying asset price models with stochastic volatility and jump discontinuities. The analytical price is derived using the Fast Fourier Transform method developed in previous literature, which enables prices to be computed quickly. This model is compared with the Black-Scholes model, and the results suggest that this model addresses a known issue with the Black-Scholes model, the under and over valuations of short maturity options. The analytical solution is also used to investigate effective control variates in Monte Carlo simulations. Simulation experiments indicate that the random motion of the asset price serves as an effective control variate.
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