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Influence of jump-at-default in IR and FX on Quanto CDS prices

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  • A. Itkin
  • V. Shcherbakov
  • A. Veygman

Abstract

We propose a new model for pricing Quanto CDS and risky bonds. The model operates with four stochastic factors, namely: hazard rate, foreign exchange rate, domestic interest rate, and foreign interest rate, and also allows for jumps-at-default in the FX and foreign interest rates. Corresponding systems of PDEs are derived similar to how this is done in Bielecki at al., 2005. A localized version of the RBF partition of unity method is used to solve these 4D PDEs. The results of our numerical experiments presented in the paper qualitatively explain the discrepancies observed in the marked values of CDS spreads traded in domestic and foreign economies.

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  • A. Itkin & V. Shcherbakov & A. Veygman, 2017. "Influence of jump-at-default in IR and FX on Quanto CDS prices," Papers 1711.07133, arXiv.org.
    • Handle: RePEc:arx:papers:1711.07133
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    References listed on IDEAS

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    1. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2015. "Multi Currency Credit Default Swaps Quanto effects and FX devaluation jumps," Papers 1512.07256, arXiv.org, revised Jan 2018.
    2. Alexander Lipton & Ioana Savescu, 2014. "Pricing credit default swaps with bilateral value adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 171-188, January.
    3. Albert Cohen & Nick Costanzino, 2017. "Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model," Risks, MDPI, vol. 5(2), pages 1-28, April.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    6. Patrick Augustin & Mikhail Chernov & Dongho Song, 2018. "Sovereign Credit Risk and Exchange Rates: Evidence from CDS Quanto Spreads," NBER Working Papers 24506, National Bureau of Economic Research, Inc.
    7. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    8. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2005. "PDE approach to valuation and hedging of credit derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 257-270.
    9. Antonis Papapantoleon, 2008. "An introduction to L\'{e}vy processes with applications in finance," Papers 0804.0482, arXiv.org, revised Nov 2008.
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    Cited by:

    1. Slobodan Milovanovi'c & Victor Shcherbakov, 2017. "Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methods," Papers 1711.09852, arXiv.org, revised Aug 2018.
    2. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2019. "Multi-Currency Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-35, June.

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