• Equity Derivatives

    Analytical proxy formulas for the price of a convertible bond

    The article studies the possibility for analytically approximating the price of a convertible bond within defaultable Markov diffusion models. Since convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea to “Europeanize” the American conversion option of the holder. Consequently, the quality of the approximations stands and falls with the value of the early conversion premium, and the resulting formulas in general may be viewed as (often quite sharp) lower bounds for the price.