Duration, convexity and other Greeks are important risk metrics in the management of convertible bond portfolio and for hedging interest rate risk, equity risk and other risks in convertible bond arbitrage strategy. Since convertible bond is a hybrid of bond and equity, the conversion feature is known to have profound impact on duration and convexity. In this thesis, I develop a two-factor pricing model for coupon bearing defaultable convertible bonds with stock price and interest rate as the stochastic state variables, where the arrival of default is modeled as a Poisson process. By using the bond price as the numeraire, the pricing formulation is reduced to an one-dimensional model. I manage to derive analytic expressions for the bond value, duration, convexity and other Greeks. The v...[ Read more ]

Duration, convexity and other Greeks are important risk metrics in the management of convertible bond portfolio and for hedging interest rate risk, equity risk and other risks in convertible bond arbitrage strategy. Since convertible bond is a hybrid of bond and equity, the conversion feature is known to have profound impact on duration and convexity. In this thesis, I develop a two-factor pricing model for coupon bearing defaultable convertible bonds with stock price and interest rate as the stochastic state variables, where the arrival of default is modeled as a Poisson process. By using the bond price as the numeraire, the pricing formulation is reduced to an one-dimensional model. I manage to derive analytic expressions for the bond value, duration, convexity and other Greeks. The value of convertible bond is found to decrease with correlation coefficient between stock price and risk-free bond value. The impact of short rate volatility on convertible value appears to be ambiguous and depends on the correlation coefficient. My analysis also reveals that the duration of convertible bond increases with coupon rate and decreases with default intensity and there is concave relationship between duration and dividend yield. In addition, the convexity of convertible bond decreases with stock price and delta of convertible bond decreases with coupon rate.