Presented by: 
Duy-Minh Dang (UQ)
Mon 14 Sep, 2:00 pm - 3:00 pm
Steele Building (03), room 262

We present a novel Monte-Carlo (MC) method for computing option prices and hedging parameters under a very general N-dimensional jump-diffusion model with stochastic variance and multi-factor stochastic interest rate(s), where N is arbitrary. The focus of our approach is variance reduction via dimension reduction achieved by utilizing a combination of the conditional MC, applied to the variance factor, and the Fourier transform techniques employed to solve the conditional Partial-Integro Differential Equation (PIDE) that arises. Under our approach, the analytical tractability of the corresponding one-dimensional jump-diffusion model is preserved, and as the result, the option price can be expressed as the expectation of an analytical solution to the conditional PIDE. All the interest rate factors are completely removed from the computation of this solution via exact integrations. Hence, our approach results in a powerful dimension reduction from N to one, which often results in a significant variance reduction as well. Our method can also neatly compute hedging parameters. Numerical results with widely used jump distributions, such as the normal and double-exponential distributions, show that the proposed method is highly efficient.