On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates
AbstractWe construct multi-currency models with stochastic volatility (SV) 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 (Hull, J. and White, A.  Pricing interest-rate derivative securities, Review of Financial Studies , 3, pp. 573--592). We then extend the framework by modelling the interest rate by an SV displaced-diffusion (DD) Libor Market Model (Andersen, L. B. G. and Andreasen, J.  Volatility skews and extensions of the libor market model, Applied Mathematics Finance , 1, pp. 1--32), 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 pay-offs.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 19 (2012)
Issue (Month): 1 (February)
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Other versions of this item:
- Grzelak, Lech & Oosterlee, Kees, 2010. "On cross-currency models with stochastic volatility and correlated interest rates," MPRA Paper 23020, University Library of Munich, Germany.
- G1 - Financial Economics - - General Financial Markets
- F3 - International Economics - - International Finance
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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