IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0711.2807.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0711.2807
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Luciano Campi & Alessandro Sbuelz, 2005. "Closed-form pricing of Benchmark Equity Default Swaps under the CEV assumption," Post-Print hal-00534284, HAL.
    2. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    4. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Other publications TiSEM f10edfa3-d4c3-489b-bffe-4, Tilburg University, School of Economics and Management.
    5. Alexander Novikov & R. E. Melchers & E. Shinjikashvili & N. Kordzakhia, 2003. "First Passage Time of Filtered Poisson Process with Exponential Shape Function," Research Paper Series 109, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Discussion Paper 2005-28, Tilburg University, Center for Economic Research.
    7. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    8. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    9. Ajay Khanna & Dilip Madan, 2004. "Understanding option prices," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 55-63.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    15. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anna Battauz & Marzia Donno & Alessandro Sbuelz, 2017. "Reaching nirvana with a defaultable asset?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 31-52, November.
    2. 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.
    3. Maclachlan, Iain C, 2007. "An empirical study of corporate bond pricing with unobserved capital structure dynamics," MPRA Paper 28416, University Library of Munich, Germany.
    4. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    5. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    6. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    7. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    8. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    9. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    10. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    11. Kazutoshi Yamazaki, 2017. "Phase-type Approximation of the Gerber-Shiu Function," Papers 1701.02798, arXiv.org.
    12. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    13. Zbigniew Palmowski & José Luis Pérez & Kazutoshi Yamazaki, 2021. "Double continuation regions for American options under Poisson exercise opportunities," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 722-771, April.
    14. Zhang, Gongqiu & Li, Lingfei, 2023. "A general method for analysis and valuation of drawdown risk," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    15. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
    16. Zhang, Xiang & Li, Lingfei & Zhang, Gongqiu, 2021. "Pricing American drawdown options under Markov models," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1188-1205.
    17. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    18. Mitya Boyarchenko & Sergei Levendorskiĭ, 2015. "Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided L�vy models: the parabolic Laplace inversion method," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 421-441, March.
    19. Hao, Xuemiao & Li, Xuan & Shimizu, Yasutaka, 2013. "Finite-time survival probability and credit default swaps pricing under geometric Lévy markets," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 14-23.
    20. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0711.2807. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.