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Pricing Equity Default Swaps under an approximation to the CGMY L\'{e}% vy Model

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  • Soeren Asmussen
  • Dilip Madan
  • Martijn Pistorius

Abstract

The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L\'{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral process for which we infer the first passage times of stock prices to 30% of the price level at contract initiation. These distributions are then used in pricing 50% recovery rate equity default swap (EDS) contracts and the resulting prices are compared with the prices of credit default swaps (CDS). An illustrative analysis is presented for these contracts on Ford and GM.

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  • Soeren Asmussen & Dilip Madan & Martijn Pistorius, 2007. "Pricing Equity Default Swaps under an approximation to the CGMY L\'{e}% vy Model," Papers 0711.2807, arXiv.org.
    • Handle: RePEc:arx:papers:0711.2807
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    2. Peter Iseger & Paul Gruntjes & Michel Mandjes, 2013. "A Wiener–Hopf based approach to numerical computations in fluctuation theory for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 101-118, August.
    3. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    4. Rafael Mendoza-Arriaga & Vadim Linetsky, 2011. "Pricing equity default swaps under the jump-to-default extended CEV model," Finance and Stochastics, Springer, vol. 15(3), pages 513-540, September.
    5. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
    6. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2009. "Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models," Papers 0911.0373, arXiv.org, revised Oct 2010.
    7. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    8. Walter Farkas & Ludovic Mathys & Nikola Vasiljevi'c, 2020. "Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps," Papers 2002.04675, arXiv.org, revised Jan 2021.
    9. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    10. Winston Buckley & Sandun Perera, 2019. "Optimal demand in a mispriced asymmetric Carr–Geman–Madan–Yor (CGMY) economy," Annals of Finance, Springer, vol. 15(3), pages 337-368, September.
    11. Masahiko Egami & Kazutoshi Yamazaki, 2010. "Solving Optimal Dividend Problems via Phase-Type Fitting Approximation of Scale Functions," Discussion papers e-10-011, Graduate School of Economics Project Center, Kyoto University.
    12. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    13. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    14. Oleg Kudryavtsev, 2024. "A simplified Wiener–Hopf factorization method for pricing double barrier options under Lévy processes," Computational Management Science, Springer, vol. 21(1), pages 1-30, June.
    15. Naser M. Asghari & Peter Iseger & Michael Mandjes, 2014. "Numerical Techniques in Lévy Fluctuation Theory," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 31-52, March.
    16. Marc Jeannin & Martijn Pistorius, 2008. "A transform approach to compute prices and greeks of barrier options driven by a class of Levy processes," Papers 0812.3128, arXiv.org, revised Mar 2009.

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