Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. (English) Zbl 1020.91030

Scott, Louis O.

Math. Finance 7, No. 4, 413-426 (1997).

Summary: 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&P500 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.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
60J65	Brownian motion

Keywords:

option pricing; stochastic volatility; jump processes; Fourier inversion