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

Grzelak, Lech and Oosterlee, Kees (2010): On cross-currency models with stochastic volatility and correlated interest rates.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Foreign-exchange (FX); stochastic volatility; Heston model; stochastic interest rates; interest rate smile; forward characteristic function; hybrids; affne diffusion; effcient calibration.
• Subjects: G - Financial Economics > G1 - General Financial Markets; F - International Economics > F3 - International Finance; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

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