A Simple and Efficient Two-Factor Willow Tree Method for Convertible Bond Pricing with Stochastic Interest Rate and Default Risk

Convertible bonds (CBs) are a popular hybrid financial instrument. CBs are difficult to price because of the correlated stochastic processes for the stock price and interest rate, embedded early exercise (conversion, call-put provision), and the credit risk of the issuer. Existing methods are either limited to some specific assumptions or are expensive in implementation and computation. In this article, we propose a simple and efficient two-factor willow tree method for convertible bond pricing. We first propose a new approach to simplify the willow tree construction so that it can be applicable to some general stochastic models. We then combine the stochastic stock price and interest rate into a two-factor tree so the CB can be priced by backward induction. The total complexity of our method is only O(N-2), much less than existing methods. Finally, our numerical experiments show the accuracy and efficiency of our method compared with the binomial tree and Monte Carlo methods.