Multilevel Monte Carlo for exponential Lévy models
将多层蒙特卡罗方法应用于指数Lévy模型下的期权定价，推导了离散监控误差的收敛率，并给出了方差伽马、NIG和α稳定过程的方差收敛率上界，数值实验验证了方法。
Abstract We apply the multilevel Monte Carlo method for option pricing problems using exponential Lévy models with a uniform timestep discretisation. For lookback and barrier options, we derive estimates of the convergence rate of the error introduced by the discrete monitoring of the running supremum of a broad class of Lévy processes. We then use these to obtain upper bounds on the multilevel Monte Carlo variance convergence rate for the variance gamma, NIG and α $\alpha$ -stable processes. We also provide an analysis of a trapezoidal approximation for Asian options. Our method is illustrated by numerical experiments.