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A flexible matrix Libor model with smiles

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  • Jos\'e Da Fonseca
  • Alessandro Gnoatto
  • Martino Grasselli

Abstract

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.

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File URL: http://arxiv.org/pdf/1203.4786
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Paper provided by arXiv.org in its series Papers with number 1203.4786.

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Date of creation: Mar 2012
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Handle: RePEc:arx:papers:1203.4786

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  1. 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, American Finance Association, vol. 52(1), pages 409-30, March.
  2. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(6), pages 591-604.
  3. Christa Cuchiero & Damir Filipovi\'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
  7. Alan Brace & Dariusz G�atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 127-155.
  8. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
  9. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  10. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(2), pages 147-185.
  11. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, American Finance Association, vol. 44(1), pages 205-09, March.
  12. 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., World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
  13. Joshi, Mark & Yang, Chao, 2011. "Fast delta computations in the swap-rate market model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(5), pages 764-775, May.
  14. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(4), pages 379-406.
  15. Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
  16. D. Brigo & F. Mercurio, 2003. "Analytical pricing of the smile in a forward LIBOR market model," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(1), pages 15-27.
  17. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(3), pages 383-410.
  18. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 28(3), pages 438-451.
  19. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
  20. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, Springer, vol. 10(2), pages 151-180, May.
  21. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 18(1), pages 135-153.
  22. Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(6), pages 815-824, June.
  23. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(1), pages 15-36, January.
  24. Kenneth J. Singleton & Len Umantsev, 2002. "Pricing Coupon-Bond Options And Swaptions In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(4), pages 427-446.
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Cited by:
  1. Francesca Biagini & Alessandro Gnoatto & Maximilian H\"artel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org.
  2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Papers 1406.4301, arXiv.org.
  3. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2014. "Recovering default risk from CDS spreads with a nonlinear filter," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 38(C), pages 87-104.

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