On a one time-step Monte Carlo simulation approach of the SABR model

Leitao Rodriguez, A.; Grzelak, L.A.; Oosterlee, C.W.

On a one time-step Monte Carlo simulation approach of the SABR model

Application to European options

Journal article (2017)

Authors

A. Leitao Rodriguez Centrum Wiskunde & Informatica (CWI), Numerical Analysis -

L.A. Grzelak Numerical Analysis - , ING

C.W. Oosterlee Centrum Wiskunde & Informatica (CWI), Numerical Analysis -

Research Group

Numerical Analysis () (TU Delft)

Copulas SABR model Computational finance Stochastic-local volatility models

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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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 alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

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