On an efficient multiple time step Monte Carlo simulation of the SABR model
提出一种多时间步蒙特卡洛模拟方法，用于在SABR随机波动率模型下为期权定价，尤其适合长期和奇异期权，是单步法的扩展，结合了傅里叶逆变换、随机配置、Gumbel copula等技巧。
<p>In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.</p>