Grzelak, Lech and Oosterlee, Kees (2010): On cross-currency models with stochastic volatility and correlated interest rates.
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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|
|Original Title:||On cross-currency models with stochastic volatility and correlated interest rates|
|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
|Depositing User:||Lech A. Grzelak|
|Date Deposited:||04. Jun 2010 10:22|
|Last Modified:||12. Feb 2013 09:16|
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