Reclaiming Quasi–Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation Through Fourier Transform
针对投资组合在险价值模拟中因指示函数不连续导致准蒙特卡洛方法效率下降的问题，提出用傅里叶变换平滑期望估计，从而恢复其快速收敛优势，数值实验显示该方法比常规蒙特卡洛和准蒙特卡洛更快更准。
Quasi–Monte Carlo methods overcome the problem of sample clustering in regular Monte Carlo simulation and have been shown to improve simulation efficiency in the derivatives pricing literature when the price is expressed as a multidimensional integration and the integrand is suitably smooth. For portfolio value-at-risk (VaR) problems, the distribution of portfolio value change is based on the expectation of an indicator function, hence the integrand is discontinuous. The purpose of this paper is to smooth the expectation estimation of an indicator function via Fourier transform so that the faster convergence rate of quasi–Monte Carlo methods can be reclaimed theoretically. Under fairly mild assumptions, the simulation of portfolio value-at-risk is fast and accurate. Numerical examples elucidate the advantage of the proposed approach over regular Monte Carlo and quasi–Monte Carlo methods.