|Jun 30, 2022
|Peking University HSBC Business School
The Broadie-Kaya exact simulation for the Heston stochastic volatility model avoids the potential large simulation bias, thus maintaining the simulation errors to be inversely proportional to the square root of the computational time budget. However, it is not competitive in accuracy-speed comparison since it is time tedious to calculate the conditional integrated variance. Glasserman and Kim speed up the computation by representing the quantity with the three-term infinite gamma series. We propose an enhanced exact simulation scheme based on Poisson conditioning so that the simulation of the terminal variance and conditional integrated variance under the Heston model can be reduced to simple simulation steps that only involve Poisson and gamma variables. Other related low-bias simulation schemes, like Tse-Wan's Inverse Gaussian and Andersen's Quadratic Exponential schemes, can be enhanced using the unified Poisson conditioning. For pricing path-dependent options using time-discretization schemes, we also propose better quadrature rules for computing integrated variance beyond the simple trapezoidal rule. Our extensive numerical tests reveal the superb performance of our exact Poisson conditioning simulation schemes in terms of accuracy, efficiency and reliability when compared with most existing simulation schemes for the Heston model.