On cross-currency models with stochastic volatility and correlated interest rates
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 23020.
Date of creation: 01 Jun 2010
Date of revision:
Foreign-exchange (FX); stochastic volatility; Heston model; stochastic interest rates; interest rate smile; forward characteristic function; hybrids; affne diffusion; effcient calibration.;
Other versions of this item:
- Lech A. Grzelak & Cornelis W. Oosterlee, 2012. "On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
- 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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