On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates

Applied Mathematical Finance Volume19, Issue 1, 2012

26 Pages Posted: 3 Jun 2010 Last revised: 21 Oct 2014

See all articles by Lech A. Grzelak

Lech A. Grzelak

Delft University of Technology

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: June 1, 2010

Abstract

We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by modeling the interest rate by a stochastic volatility displaced-diffusion Libor Market Model [AA02], which can model an interest rate smile. We provide semi-closed form approximations which lead to efficient calibration of the multi-currency models. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity-FX-interest rate hybrid payoffs.

Keywords: Foreign-exchange (FX), stochastic volatility, Heston model, stochastic interest rates, interest rate smile, forward characteristic function, hybrids, affne diffusion, effcient calibration

JEL Classification: G12, G13

Suggested Citation

Grzelak, Lech Aleksander and Oosterlee, Cornelis W., On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates (June 1, 2010). Applied Mathematical Finance Volume19, Issue 1, 2012 , Available at SSRN: https://ssrn.com/abstract=1618684 or http://dx.doi.org/10.2139/ssrn.1618684

Lech Aleksander Grzelak (Contact Author)

Delft University of Technology ( email )

Netherlands
00310655731315 (Phone)

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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