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Keywords:

  • option pricing;
  • stochastic volatility;
  • jump processes;
  • Fourier inversion

Fast closed form solutions for prices on European stock options are developed in a jump-diffusion model with stochastic volatility and stochastic interest rates. The probability functions in the solutions are computed by using the Fourier inversion formula for distribution functions. The model is calibrated for the S and P 500 and is used to analyze several effects on option prices, including interest rate variability, the negative correlation between stock returns and volatility, and the negative correlation between stock returns and interest rates.