A Short Note on the Exact Stochastic Simulation Scheme of the Hull-White Model and Its Implementation

18 Pages Posted: 25 Feb 2016 Last revised: 23 May 2016

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Date Written: February 21, 2016

Abstract

In this short note we derive an exact simulation scheme for the joint distribution of (r(t),N(t)), where r denotes the short rate following a Hull-White model and $N$ denotes the numeraire.

To sample the correct joint distribution of (r(t),N(t)) our scheme requires a two-factor Brownian driver. In other words: the time-discrete Hull-White model is a two factor model.

We investigate the performance of this scheme compared to the classical schemes for correlation dependent products like the LIBOR in arrears and Bermudan swaptions. We show that the exact sampling of the joint distribution is important in some applications, e.g., the valuation of Bermudan options using American Monte-Carlo method. Traditional approximation of the numeraire may generate biases if the model uses larger simulation time-steps.

Large time-step simulation of short rate models and the American Monte-Carlo method is of interest in the calculation of portfolio effects (xVAs), where usually many risk factors have to be simulated and computational resources need to be saved.

Keywords: Hull-White model, Monte-Carlo simulation, Euler scheme, Exact scheme

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., A Short Note on the Exact Stochastic Simulation Scheme of the Hull-White Model and Its Implementation (February 21, 2016). Available at SSRN: https://ssrn.com/abstract=2737091 or http://dx.doi.org/10.2139/ssrn.2737091

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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