Pricing and Hedging Convertible Bonds Under Non-probabilistic Interest Rates

Two of the authors (DE and PW) recently introduced a non-probabilistic spot interest rate model. The key concepts in this model are the non-diffusive nature of the spot rate process and the uncertainty in the parameters. The model assumes the worst possible outcome for the spot rate path when pricing a fixed-income product. The model differs in many important ways from the traditional approaches of fully deterministic rates (as assumed when calculating yields, durations and convexities) or stochastic rates governed by a Brownian motion. In this new model, delta hedging and unique pricing play no role, nor does any market price of risk term appear. In this paper we apply the model to the pricing of convertible bonds. Later we show how to optimally hedge the interest rate risk; this hedging is not dynamic but static. We show how to solve the governing equation numerically and present results.