On the Binomial-Tree Approach to Convertible Bonds Pricing and Risk Assessment

In this chapter we concentrate at the most popular model for convertible bond (CB) valuation in a one-factor, stochastic underlying stock price setting. Through the last decade, the Tsiveriotis–Fernandes model (1998) has become a widely commented model that involves the state of default of the issuer of the CB. A routine approach to the solution of this model is the usage of methods of finite difference schemes (FDS). However, for many people trained in finance these methods are not very intuitive and they tend to ignore them and prefer to use binomial-tree approach as more intuitive technique. For that reason, our primary focus is to highlight the answer of the so far unanswered question: Does the binomial-tree approach to CBs provide accurate pricing, hedging, and risk assessment? We show on a set of representative examples that by using binomial-tree methodology one is unable to provide a consistent analysis of the pricing, hedging, and risk assessment. We start the chapter with the basics of CBs and CB market. We then explain the implementation of TF model within binary-tree approach. We conclude the chapter with performance valuation of binomial-tree approach showing unexpected behavior in practice areas such as pricing (profile of CB's price versus underlying stock price), hedging (performance of CB's delta, gamma, and convertible arbitrage strategy versus underlying stock), and risk assessment (Monte Carlo VaR with respect to the underlying).