This study proposes an approximation of European option prices under arbitrary diffusion processes of the spot price. The key is to approximate the characteristic function of the log spot price process as the solution to ordinary differential equations. The option price is then obtained by the inverse Fourier transform. Numerical experiments, using a model that has the constant elasticity of volatility specification in both the spot price and volatility processes, confirm reasonable accuracy of the approximation, except when the volatility process exhibits high variation.
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