On cross-currency models with stochastic volatility and correlated interest rates

Lech Grzelak and Cornelis Oosterlee

MPRA Paper from University Library of Munich, Germany

Abstract: We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We frst 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 effcient 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. (search for similar items in EconPapers)
JEL-codes: F3 G1 G13 (search for similar items in EconPapers)
Date: 2010-06-01
New Economics Papers: this item is included in nep-ifn
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Citations: View citations in EconPapers (9)

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