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
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
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