Abstract and Applied Analysis

Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy

Haiyang Wang and Zhen Wu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. We also obtain the optimal conversion time when there is no dividends-paying for underlying common stocks. Furthermore, we consider the case that the loan rate is higher than riskless interest rate in a financial market, and conclude that it does not affect the price of convertible bonds actually. To illustrate our results, some numerical simulations are given and discussed at last.

Article information

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 341519, 9 pages.

First available in Project Euclid: 6 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Wang, Haiyang; Wu, Zhen. Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 341519, 9 pages. doi:10.1155/2014/341519. https://projecteuclid.org/euclid.aaa/1412605856

Export citation


  • O. H. Poensgen, “The valuation of convertible bonds–-part 1,” Industrial Management Review, vol. 7, pp. 77–92, 1965.
  • O. H. Poensgen, “The valuation of convertible bonds–-part 2,” Industrial Management Review, vol. 7, pp. 83–98, 1966.
  • W. J. Baumol, B. G. Malkiel, and R. E. Quandt, “The valuation of convertible securities,” Quarterly Journal of Economics, vol. 40, pp. 48–59, 1966.
  • R. Weil, J. E. Segall, and D. Green, “Premiums on convertible bonds,” Journal of Finance, vol. 23, pp. 445–463, 1968.
  • F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, pp. 637–654, 1973.
  • J. E. Ingersoll Jr., “A contingent-claims valuation of convertible securities,” Journal of Financial Economics, vol. 4, no. 3, pp. 289–321, 1977.
  • M. J. Brennan and E. S. Schwartz, “Convertible bonds: valuation and optimal strategies for call and conversion,” Journal of Finance, vol. 32, pp. 1699–1715, 1977.
  • M. J. Brennan and E. S. Schwartz, “Analyzing convertible bonds,” Journal of Financal and Quantitative Analysis, vol. 15, pp. 907–929, 1980.
  • J. J. McConnell and E. S. Schwartz, “LYON taming,” Journal of Finance, vol. 41, pp. 561–576, 1986.
  • T. S. Y. Ho and D. M. Pfeffer, “Convertible bonds: model, value attribution, and analytics,” Financial Analysts Journal, vol. 52, no. 5, pp. 35–44, 1996.
  • K. Tsiveriotis and C. Fernandes, “Valuing convertible bonds with credit risk,” Journal of Fixed Income, vol. 8, pp. 95–102, 1998.
  • E. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems and Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
  • D. Duffie and L. G. Epstein, “Stochastic differential utility,” Econometrica, vol. 60, no. 2, pp. 353–394, 1992.
  • S. G. Peng, “Probabilistic interpretation for systems of quasilinear parabolic partial differential equations,” Stochastics and Stochastics Reports, vol. 37, no. 1-2, pp. 61–74, 1991.
  • N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
  • T. R. Bielecki, S. Crépey, M. Jeanblanc, and M. Rutkowski, “Arbitrage pricing of defaultable game options with applications to convertible bonds,” Quantitative Finance, vol. 8, no. 8, pp. 795–810, 2008.
  • N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M. C. Quenez, “Reflected solutions of backward SDE's, and related obstacle problems for PDE's,” The Annals of Probability, vol. 25, no. 2, pp. 702–737, 1997.
  • X. Guo and H. Y. Wang, “Dividends sharing convertible bonds pricing and numerical evaluation,” Mathematical Problems in Engineering, vol. 2013, Article ID 932579, 10 pages, 2013.
  • D. Nualart, The Malliavin Calculus and Related Topics, Probability and Its Applications, Springer, New York, NY, USA, 1995.
  • N. El Karoui, E. Pardoux, and M. C. Quenez, “Reflected backward SDEs and American options,” in Numerical Methods in Finance, vol. 13, pp. 215–231, Cambridge University Press, Cambridge, Mass, USA, 1997. \endinput