In order to construct a model to price convertible bonds, a hybrid security with complicated provisions, this study concentrates on the way of depicting the equity and the default process. The Constant Elasticity of Variance model (CEV model) which modifies the assumption of constant volatility to capture the negative relationship between the stock price and the variance is applied. The default process integrates the information from both equity and debt market by setting the default intensity model to endogenize the default process into the pricing model.
The tree structure is built by a manner of variable transformation. After considering all information and deciding whether the provisions to be executed on each node, then the value of convertible bond could be calculated in a backward-induction fashion. Two trading convertible bonds are chosen to examine the practicality of this model and the empirical result shows that this model fit the market value well. The sensitivity analysis suggests that the coefficient of leverage effect does affect the value of convertible bond in an inverse direction and other parameters are not significantly sensitive to the value of convertible bond.

1. Ayache, E., P.A. Forsyth, and K.R. Vetzal (2003). “Valuation of Convertible Bonds with Credit Risk”, Journal of Derivatives, 11, 1, 9–29.
2. Beckers, S. (1980). “The constant elasticity of variance model and its implications for option pricing”, Journal of Finance, 35, 661–673.
3. Brennan, M. J. and E.S. Schwartz (1977). "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion", Journal of Finance, 32, 1699–1715.
4. Brennan, M. J. and E.S. Schwartz (1980). "Analyzing Convertible Securities", Journal of Financial and Quantitative Analysis, XV, 4, 907–929.
5. Brigham, E. F. (1966). “An Analysis of Convertible Debentures: Theory and Some Empirical Evidence”, Journal of Finance, 21, 35–54.
6. Carayannopoulos, P. and M. Kalimipalli (2003). “Convertible Bonds and Pricing Biases", Journal of Fixed Income, 13, 3, 64–73.
7. Chamber, D. and Q. Lu (2007). “A Tree Model for Pricing Convertible Bond with Equity, Interest Rate, and Default Risk”, Journal of Derivatives, 14, 4, 25–46.
8. Cox, J. (1975) “Notes on option pricing I: constant elasticity of variance diffusions”, Working Paper, Stanford University.
9. Das S.R., and R.K. Sundaram (2007). “An Integrated Model for Hybrid Securities”, Management Science, 53, 1439–1451.
10. Derman, E. (1994). “Valuing Convertible Bonds as Derivatives”, Technical report, Goldman Sachs.
11. Hung, M.W. and J.Y. Wang (2002). “Pricing Convertible Bond Subject to Default Risk”, Journal of Derivatives, 10, 2, 75–87.
12. Ingersoll, J. (1977). “An Examination of Corporate Call Policies on Convertible Securities”, Journal of Finance, 32, 463– 478.
13. Kang, JK., and Yul W. Lee (1996). “The Pricing of Convertible Debt Offerings”, Journal of Financial Economics, 41, 2, 231–248.
14. Liu, C.H. (2009). “Valuation of Convertible Bonds with Credit Risk”, National Cheng Chi University, Dep. of Money and Banking, Master Thesis.
15. McConnell J. J. and E. S. Schwartz (1986). “LYON Taming”, Journal of Finance, 41, 561–576.
16. Nelson, D. and K. Ramaswamy (1990). “Simple Binomial Processes as Diffusion Approximations in Financial Models,” The Review of Financial Studies, 3, 3, 393-430.
17. Nyborg, K. G. (1996). “The Use and Pricing of Convertible Bonds”, Applied Mathematical Finance, 3, 167–190.
18. Schmalensee R. and R. R. Trippi (1978). “Common stock volatility expectations implied by option premia.” Journal of Finance, 33, 129–147.
19. Tsiveriotis, K. and C. Fernandes (1998). “Valuing Convertible Bonds with Credit Risk”, Journal of Fixed Income, 8, 3, 95–102.