An analytic multi-currency model with stochastic volatility and stochastic interest rates
AbstractWe introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinity of the model Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fit simultaneously FX implied volatilities while being coherent with interest rate products.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.7246.
Date of creation: Feb 2013
Date of revision: Mar 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-02 (All new papers)
- NEP-CBA-2013-03-02 (Central Banking)
- NEP-IFN-2013-03-02 (International Finance)
- NEP-MON-2013-03-02 (Monetary Economics)
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- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010.
"FX Smile in the Heston Model,"
- Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010. "FX Smile in the Heston Model," MPRA Paper 25491, University Library of Munich, Germany.
- Agnieszka Janek & Tino Kluge & Rafał Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," SFB 649 Discussion Papers SFB649DP2010-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
- David Heath & Eckhard Platen, 2005.
"Currency Derivatives Under A Minimal Market Model With Random Scaling,"
International Journal of Theoretical and Applied Finance (IJTAF),
World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1157-1177.
- David Heath & Eckhard Platen, 2005. "Currency Derivatives under a Minimal Market Model with Random Scaling," Research Paper Series 154, Quantitative Finance Research Centre, University of Technology, Sydney.
- Marco Bianchetti, 2009. "Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," Papers 0905.2770, arXiv.org, revised Jul 2012.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
- Hurd, Matthew & Salmon, Mark & Schleicher, Christoph, 2005.
"Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index,"
CEPR Discussion Papers
5114, C.E.P.R. Discussion Papers.
- Matthew Hurd & Mark Salmon & Christoph Schleicher, 2007. "Using copulas to construct bivariate foreign exchange distributions with an application to the sterling exchange rate index," Bank of England working papers 334, Bank of England.
- Christoph Schleicher & Matthew Hurd & Mark Salmon, 2005. "Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index," Computing in Economics and Finance 2005 215, Society for Computational Economics.
- Griselda Deelstra & Gr\'egory Ray\'ee, 2012.
"Local Volatility Pricing Models for Long-dated FX Derivatives,"
- Griselda Deelstra & Grégory Rayée, 2013. "Local Volatility Pricing Models for Long-Dated FX Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
- Schlögl, Erik, 2013. "Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 611-632.
- Peter Carr & Liuren Wu, 2004.
"Stochastic Skew in Currency Options,"
- Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
- Fries, Christian P., 2010. "Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization," MPRA Paper 23082, University Library of Munich, Germany, revised 30 May 2010.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Alessandro Gnoatto, 2012. "The Wishart short rate model," Papers 1203.5513, arXiv.org.
- JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
- Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
- Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
- Masaaki Kijima & Keiichi Tanaka & Tony Wong, 2009. "A multi-quality model of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 133-145.
- Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.
- Grzelak, Lech & Oosterlee, Kees, 2010.
"On cross-currency models with stochastic volatility and correlated interest rates,"
23020, University Library of Munich, Germany.
- 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.
- Christoph Schleicher & Mark Salmon, 2006. "Pricing Multivariate Currency Options with Copulas," Working Papers wp06-21, Warwick Business School, Finance Group.
- Walter Schachermayer & Josef Teichmann, 2008. "How Close Are The Option Pricing Formulas Of Bachelier And Black-Merton-Scholes?," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 155-170.
- Rehez Ahlip, 2008. "Foreign Exchange Options Under Stochastic Volatility And Stochastic Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 277-294.
- Alessandro Gnoatto, 2012. "The Wishart Short Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1250056-1-1.
- Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
- Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
- Alexander van Haastrecht & Antoon Pelsser, 2011. "Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 665-691.
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