On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates
We 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. [1990] Pricing interest-rate derivative securities, <italic>Review of Financial Studies</italic>, 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. [2000] Volatility skews and extensions of the libor market model, <italic>Applied Mathematics Finance</italic>, 1[7], 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.
Year of publication: |
2012
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Authors: | Grzelak, Lech A. ; Oosterlee, Cornelis W. |
Published in: |
Applied Mathematical Finance. - Taylor & Francis Journals, ISSN 1350-486X. - Vol. 19.2012, 1, p. 1-35
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Publisher: |
Taylor & Francis Journals |
Saved in:
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