A Simple and Precise Method for Pricing Convertible Bond with Credit Risk

Xiao, Tim (2014): A Simple and Precise Method for Pricing Convertible Bond with Credit Risk. Forthcoming in: Journal of Derivatives and Hedge Funds , Vol. 19, No. 4 (8 February 2014): pp. 244-258.

Abstract

This paper presents a new framework for valuing hybrid defaultable financial instruments, for example, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price.

• Item Type: MPRA Paper
• Language: English
• Keywords: hybrid financial instrument, convertible bond, convertible underpricing, convertible arbitrage, default time approach (DTA), default probability approach (DPA), jump diffusion.
• Subjects: G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Agarwal, V., Fung, W., Loon, Y. and Naik, N. (2007) Liquidity provision in the convertible bond market: analysis of convertible arbitrage hedge funds. CFR-working paper.

Ammann, M., Kind, A., and Wilde, C. (2003) Are convertible bonds underpriced? An analysis of the French market. Journal of Banking & Finance 27: 635-653.

Ammann, M, Kind, A., and Wilde, C. (2008) Simulation-based pricing of convertible bonds. Journal of empirical finance, 15: 310-331.

Andersen, L. and Buffum, D. (2004) Calibration and implementation of convertible bond models. Journal of Computational Finance 7: 1-34.

Ayache, E., Forsyth, P. A., and Vetzal, K. R. (2003) The valuation of convertible bonds with credit risk. Journal of Derivatives 11: 9-30.

Batta, G., Chacko, G. and Dharan, B. (2007) Valuation consequences of convertible debt issuance. Working paper.

Bloomberg (2009) OVCV model description. Quantitative research and development, Equities team.

Brennan, M. and Schwartz, E. (1980) Analyzing convertible bonds. Journal of Financial and Quantitative Analysis 15: 907-929.

Calamos, N. P. (2011) Convertible arbitrage: Insights and techniques for successful hedging. John Wiley & Sons.

Carr, P. and Linetsky, V. (2006) A jump to default extended CEV model: an application of Bessel processes. Finance and Stochastics 10: 303-330.

Carayannopoulos, P. and Kalimipalli, M. (2003) Convertible bond prices and inherent biases. Journal of Fixed Income 13: 64-73.

Choi, D., Getmansky, M. and Tookes, H. (2009) Convertible bond arbitrage, liquidity externalities, and stock prices. Journal of Financial Economics 91: 227-251.

Davis, M. and Lischka, F. R. (1999) Convertible bonds with market risk and credit risk. Working paper, Tokyo-Mitsubishi International plc.

Duffie, D., and Huang, M. (1996) Swap rates and credit quality. Journal of Finance 51: 921-949.

Duffie, D., and Singleton, K. J. (1999) Modeling term structure of defaultable bonds. Review of Financial Studies 12: 687-720.

Ederington, L. and Lee, H. (1993) How markets process information: News releases and volatility. Journal of Finance 48: 1161-1191.

Grimwood, R., and Hodges, S. (2002) The valuation of convertible bonds: a study of alternative pricing models. Working paper, Warwick University.

Goldman Sachs (1994) Valuing convertible bonds as derivatives. Quantitative Strategies Research Notes, Goldman Sachs.

Hull, J. (2003) Options, Futures and Other Derivatives (5th ed.). Prentice Hall, Upper Saddle River, NJ.

Jarrow, R. A. and Protter, P. (2004) Structural versus reduced form models: a new information based perspective. Journal of Investment Management 2: 34-43.

Loncarski, I., Horst, J. and Veld C. (2009) The rise and demise of the convertible arbitrage strategy. Financial Analysts Journal 26: 35-50.

Merton, R. C. (1976) Option pricing when underlying stock returns are discontinuous. Journal of Financial Economy 3: 125-144.

J. P. Morgan (1999) The J. P. Morgan guide to credit derivatives. Risk Publications.

J.P. Morgan (2001) Par credit default swap spread approximation from default probabilities. Risk Publications.

Somanath, V.S. (2011) International financial management. I.K. International Publishing House Pvt. Ltd.

Tsiveriotis, K. and Fernandes, C. (1998) Valuing convertible bonds with credit risk. Journal of Fixed Income 8: 95–102.

Xiao, T. (2013) An accurate solution for credit value adjustment (CVA) and wrong way risk. Working paper.

Zabolotnyuk, Y., Jones, R., and Veld, C., (2010), “An empirical comparison of convertible bond valuation models,” Financial Management, 39, 2, 675-705.