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Pricing of CDS Options with the HJM approach: a Numerical Implementation


  • Viviana Fanelli


  • Silvana Musti



This paper provides CDS option pricing in a probability setting equipped with a subfiltration structure. The evolution of the defaultable term structure is modelled using the approach developed in Heath et al. (1992) when the spot rate and the forward rate affect the volatility term. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical algorithm for pricing. Finally, the Antithetic Variables technique is used to reduce the variance of estimations.

Suggested Citation

  • Viviana Fanelli & Silvana Musti, 2007. "Pricing of CDS Options with the HJM approach: a Numerical Implementation," Quaderni DSEMS 26-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
  • Handle: RePEc:ufg:qdsems:26-2007

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    References listed on IDEAS

    1. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    2. 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: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    5. 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..
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    More about this item


    HJM model; Cox process; Monte Carlo method; CDS option;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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