ANALYTICS OF DURATION AND CONVEXITY FOR BONDS WITH EMBEDDED OPTIONS: THE CASE OF CONVERTIBLES

Most recent advances in the application of duration and convexity to bond valuation focus on option free bonds or the so-called "plain vanilla" variety. As yet, no one has provided an adequate analytical formulation of duration and convexity for convertible bonds. The price behavior of a convertible bond differs from a nonconvertible bond because the convertible's price reflects the underlying value of the issuing firm's common stock, as well as changes in market interest rates. A convertible bond possesses greater positive convexity than a comparable callable bond because of the inclusion of the call option. This unique feature of convertibles makes their cash flows and maturities uncertain, and thus the simple duration-convexity of a pure bond is an insufficient proxy for the duration-convexity of a convertible bond. A method for estimating duration and convexity for convertible bonds is presented. Further, the measures of duration and convexity for convertible bonds developed provide a testable hypothesis about the timing of a company's exercise of its call option on convertible debt.