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On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Álvaro Leitao, Lech A. Grzelak and Cornelis Oosterlee

Applied Mathematics and Computation, 2017, vol. 293, issue C, 461-479

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.

Keywords: Computational finance; Stochastic-local volatility models; SABR model; Copulas (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.amc.2016.08.030

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