In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alter- native to Hagan’s analytic formula for short maturities that may be employed for model calibration purposes.
Computational finance, Stochastic-local volatility models, SABR model, Copulas
Computation (theme 10)
Applied Mathematics and Computation
Scientific Computing

Leitao Rodriguez, Á, Grzelak, L.A, & Oosterlee, C.W. (2017). On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options. Applied Mathematics and Computation, 293, 461–479. doi:`10.1016/j.amc.2016.08.030