Calibration and Monte Carlo Pricing of the SABR-Hull-White Model for Long-Maturity Equity Derivatives

The Journal of Computational Finance (79–113) Volume 15/Number 4, Summer 2012

24 Pages Posted: 25 Feb 2011 Last revised: 11 Nov 2014

See all articles by Bin Chen

Bin Chen

Center for Mathematics and Computer Science (CWI); Derivative Research & Validation, Rabobank International

Lech A. Grzelak

Delft University of Technology

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: February 23, 2011

Abstract

We model the joint dynamics of stock and interest rate by a hybrid SABR-Hull-White model, in which the asset price dynamics are modeled by the SABR model and the interest rate dynamics by the Hull-White short-rate model. We propose a projection formula, mapping the SABR-HW model parameters onto the parameters of the nearest SABR model. A time-dependent parameter extension of this SABR-HW model is adopted to make the calibration of the model consistent across maturity times. The calibration procedure is then finalized by employing the weighted Monte Carlo technique. The Monte Carlo weights are not uniform and chosen to replicate the calibration market instruments.

Keywords: hybrid SABR-HW model, calibration, model approximation, weighted Monte Carlo method

JEL Classification: G13

Suggested Citation

Chen, Bin and Grzelak, Lech Aleksander and Oosterlee, Cornelis W., Calibration and Monte Carlo Pricing of the SABR-Hull-White Model for Long-Maturity Equity Derivatives (February 23, 2011). The Journal of Computational Finance (79–113) Volume 15/Number 4, Summer 2012, Available at SSRN: https://ssrn.com/abstract=1768802 or http://dx.doi.org/10.2139/ssrn.1768802

Bin Chen (Contact Author)

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

Derivative Research & Validation, Rabobank International ( email )

Utrecht 3500 HG
Netherlands

Lech Aleksander Grzelak

Delft University of Technology ( email )

Netherlands
00310655731315 (Phone)

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands