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Modelling the Evolution of Credit Spreads Using the Cox Process Within the HJM Framework A CDS Option Pricing Model

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In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a sub filtration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical algorithm for pricing. Finally, the Antithetic Variable technique is used to reduce the variance of credit default swap option prices.

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  • Carl Chiarella & Viviana Fanelli & Silvana Musti, 2009. "Modelling the Evolution of Credit Spreads Using the Cox Process Within the HJM Framework A CDS Option Pricing Model," Research Paper Series 255, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:255
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    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. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. 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..
    4. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    5. Robert Jarrow, 2017. "Operational Risk," World Scientific Book Chapters, in: THE ECONOMIC FOUNDATIONS OF RISK MANAGEMENT Theory, Practice, and Applications, chapter 8, pages 69-70, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. Chunsheng Zhou, 1997. "A jump-diffusion approach to modeling credit risk and valuing defaultable securities," Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System (U.S.).
    8. 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..
    9. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2000. "A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives," Management Science, INFORMS, vol. 46(1), pages 46-62, January.
    10. 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..
    11. 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..
    12. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    13. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    14. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Viviana Fanelli & Silvana Musti, 2007. "Modelling Credit Spreads evolution using the Cox Process within the HJM framework," Quaderni DSEMS 27-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    17. Chen, Ren-Raw & Cheng, Xiaolin & Fabozzi, Frank J. & Liu, Bo, 2008. "An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(1), pages 123-160, March.
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    Cited by:

    1. Fanelli, Viviana & Maddalena, Lucia & Musti, Silvana, 2016. "Modelling electricity futures prices using seasonal path-dependent volatility," Applied Energy, Elsevier, vol. 173(C), pages 92-102.
    2. Lee, Shyan Yuan & Chiou, Wan-Jiun Paul & Chung, Yi-Fang, 2017. "Pricing corporate bonds and constructing credit curves in a developing country: The case of the Taiwan bond fund crisis," International Review of Economics & Finance, Elsevier, vol. 50(C), pages 261-274.
    3. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos Sklibosios, 2013. "Credit Derivatives Pricing With Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-28.
    4. Mohamed Ben Alaya & Ahmed Kebaier & Djibril Sarr, 2024. "Credit Spreads' Term Structure: Stochastic Modeling with CIR++ Intensity," Papers 2409.09179, arXiv.org.
    5. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    6. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
    7. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    8. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    9. Fanelli, Viviana, 2016. "A defaultable HJM modelling of the Libor rate for pricing Basis Swaps after the credit crunch," European Journal of Operational Research, Elsevier, vol. 249(1), pages 238-244.
    10. Alessandro Andreoli & Luca Vincenzo Ballestra & Graziella Pacelli, 2018. "Pricing Credit Default Swaps Under Multifactor Reduced-Form Models: A Differential Quadrature Approach," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 379-406, March.
    11. Changqing Luo & Mengzhen Li & Zisheng Ouyang, 2016. "An empirical study on the correlation structure of credit spreads based on the dynamic and pair copula functions," China Finance Review International, Emerald Group Publishing Limited, vol. 6(3), pages 284-303, August.
    12. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    13. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.
    14. Wang, Chuan-Ju & Dai, Tian-Shyr & Lyuu, Yuh-Dauh, 2014. "Evaluating corporate bonds with complicated liability structures and bond provisions," European Journal of Operational Research, Elsevier, vol. 237(2), pages 749-757.
    15. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

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    More about this item

    Keywords

    pricing; HJM model; Cox process; Monte Carlo method; CDS option;
    All these keywords.

    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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