Advertisement

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
  • 46 Downloads

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.

Keywords

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

References

  1. Bao, J., & Pan, J. (2013). Bond illiquidity and excess volatility. The Review of Financial Studies, 26(12), 30683103.CrossRefGoogle Scholar
  2. Bayraktar, E. (2008). Pricing options on defaultable stocks. Applied Mathematical Finance, 15, 277–304.CrossRefGoogle Scholar
  3. Bayraktar, E., & Yang, B. (2011). A unified framework for pricing credit and equity derivatives. Mathematical Finance, 21, 493–517.CrossRefGoogle Scholar
  4. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–54.CrossRefGoogle Scholar
  5. Cao, C., Yu, F., & Zhong, Z. (2010). The information content of option-implied volatility for credit default swap valuation. Journal of Financial Markets, 13, 321–343.CrossRefGoogle Scholar
  6. Crosbie, P. J., & Bohn, J. R. (1997). Modeling default risk. San Francisco, CA: KMV Corporation.Google Scholar
  7. Hull, J., & White, A. (1990). Pricing interest rate derivative securities. Review of Financial Studies, 3, 573–592.CrossRefGoogle Scholar
  8. Kelly, B. T., Manzo, G., & Palhares, D. (2017). Credit-implied volatility, Chicago Booth Research Paper, No. 17-12.Google Scholar
  9. Lando, D. (1998). On Cox processes and credit risky securities. Review of Derivatives Research, 2, 99–120.Google Scholar
  10. Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–70.Google Scholar
  11. RiskMetrics. (1996). Technical Document - Technical report J.P. Morgan.Google Scholar
  12. Russo, V., & Fabozzi, F. J. (2016). Pricing coupon bond options and swaptions under the two-factor Hull-White model. Journal of Fixed Income, 25, 76–82.CrossRefGoogle Scholar
  13. Zheng, C. K. (1999). Default implied volatility for credit spread.  https://doi.org/10.2139/ssrn.163848.

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

Personalised recommendations