Annals of Operations Research

, Volume 275, Issue 2, pp 669–683 | Cite as

Market implied volatilities for defaultable bonds

  • Vincenzo Russo
  • Rosella GiacomettiEmail author
  • Frank J. Fabozzi
S.I. : Application of O. R. to Financial Markets


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.


Defaultable bonds’ implied volatility Credit default swap (CDS) Merton model Hull and White model 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Head of Unit - Group Risk Management at Assicurazioni Generali S.p.A.MilanItaly
  2. 2.Department of Management, Economics and Quantitative MethodsUniversity of BergamoBergamoItaly
  3. 3.EDHEC Business SchoolNiceFrance

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