A flexible matrix Libor model with smiles
We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numerical exercise illustrates the flexibility of Wishart Libor model in describing the movements of the implied volatility surface.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, September.
- Kenneth J. Singleton & Len Umantsev, 2002. "Pricing Coupon-Bond Options And Swaptions In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 427-446.
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016.
"Stochastic correlation and risk premia in term structure models,"
Journal of Empirical Finance,
Elsevier, vol. 37(C), pages 59-78.
- Carl Chiarella & Chih-Ying Hsiao & Thuy-Duong To, 2011. "Stochastic Correlation and Risk Premia in Term Structure Models," Research Paper Series 298, Quantitative Finance Research Centre, University of Technology, Sydney.
- Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
- Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
- Joshi, Mark & Yang, Chao, 2011. "Fast delta computations in the swap-rate market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 764-775, May.
- Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
- Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
- José Da Fonseca & Martino Grasselli & Florian Ielpo, 2011. "Hedging (Co)Variance Risk With Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
- Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994.
"Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Discussion Paper Serie B
308, University of Bonn, Germany.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
- Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 37, May.
- Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
- José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
- 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.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153.
- D. Brigo & F. Mercurio, 2003. "Analytical pricing of the smile in a forward LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 15-27.
- Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
- Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
- 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.
- Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
- JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- 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.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1203.4786. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.