Pricing and Hedging Convertible Bonds under Non-Probabilistic Interest Rates

Abstract

Many different models for the behavior of interest rates have been proposed and investigated over the years. We have made progress in the sense that some formerly popular models have been eliminated from serious consideration, but there is still no general agreement on which model is the best. The uncertainty leads to substantial model risk in pricing and hedging interest rate derivatives. This article presents a different approach: rather than specifying a particular stochastic process for the short-term interest rate, Epstein, Haber, and Wilmott simply place bounds on its behavior, in the form of maximum and minimum feasible values and a constraint on its rate of change, while permitting any movement of the rate within the constraints. This general approach leads to an acceptable range for the interest rate and for financial instruments based upon it. Model dependence is greatly reduced in this way. The next challenge will be to develop models in this framework that produce tight enough bounds to be useful for traders and investors.