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Market implied volatilities for defaultable bonds

Author

Listed:
  • Vincenzo Russo

    (Head of Unit - Group Risk Management at Assicurazioni Generali S.p.A.)

  • Rosella Giacometti

    (University of Bergamo)

  • Frank J. Fabozzi

    (EDHEC Business School)

Abstract

Typically, implied volatilities for defaultable instruments are not available in the financial market since quotations related to options on defaultable bonds or on credit default swaps are usually not quoted by brokers. However, an estimate of their volatilities is needed for pricing purposes. In this paper, we provide a methodology to infer market implied volatilities for defaultable bonds using equity implied volatilities and CDS spreads quoted by the market in relation to a specific issuer. The theoretical framework we propose is based on the Merton’s model under stochastic interest rates where the short rate is assumed to follow the Hull–White model. A numerical analysis is provided to illustrate the calibration process to be performed starting from financial market data. The market implied volatility calibrated according to the proposed methodology could be used to evaluate options where the underlying is a risky bond, i.e. callable bond or other types of credit-risk sensitive financial instruments.

Suggested Citation

  • Vincenzo Russo & Rosella Giacometti & Frank J. Fabozzi, 2019. "Market implied volatilities for defaultable bonds," Annals of Operations Research, Springer, vol. 275(2), pages 669-683, April.
    • Handle: RePEc:spr:annopr:v:275:y:2019:i:2:d:10.1007_s10479-018-3064-z
    DOI: 10.1007/s10479-018-3064-z
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    References listed on IDEAS

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    1. 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.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    3. 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.
    4. E. Bayraktar, 2008. "Pricing Options on Defaultable Stocks," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 277-304.
    5. Cao, Charles & Yu, Fan & Zhong, Zhaodong, 2010. "The information content of option-implied volatility for credit default swap valuation," Journal of Financial Markets, Elsevier, vol. 13(3), pages 321-343, August.
    6. Jack Bao & Jun Pan, 2013. "Bond Illiquidity and Excess Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 26(12), pages 3068-3103.
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