On an Efficient Multiple Time-Step Monte Carlo Simulation of the SABR Model
Quantitative Finance 17(10): 1549-1565, 2017
28 Pages Posted: 17 Apr 2016 Last revised: 28 Oct 2018
Date Written: April 12, 2016
In this paper, we will present a multiple time-step Monte Carlo simulation technique for pricing options under the (Stochastic Alpha Beta Rho (SABR)) model. The proposed method is an extension of the one time-step Monte Carlo method that we proposed in an accompanying paper, for pricing European options in the context of the model calibration. A highly efficient method results, with many highly 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.
Keywords: SABR model; Exact simulation; Monte Carlo methods; Copulas; Stochastic collocation; Fourier techniques; Exotic options
JEL Classification: C15; C63
Suggested Citation: Suggested Citation