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Faster Pricing of Convertible Bonds

We study the pricing of convertible bonds using one-factor methods. Classical numerical algorithms based on lattice trees converge slowly as the number of time-steps increases when there is an issuer call. We describe an improved algorithm that has a much better rate of convergence. Our algorithm also evaluates accurately other options having a trigger level, such as barrier options. The algorithm is robust and yields smooth prices and Greek parameters as the spot approaches the trigger level. It is simple to implement and has essentially the same running time as a lattice tree algorithm.