Pricing Barrier Options with One-Factor Interest Rate Models

Abstract

Pricing barrier options for interest rates and interest-dependent securities is harder than for equities, because interest rate processes typically require more complicated models than stock returns. Even single-factor models need to incorporate the initial yield curve in order to prevent apparent arbitrage opportunities among observed bond prices in the market. When closed-form solutions do not exist, numerical valuation techniques are required, and both lattice-based approaches and Monte Carlo simulation are in common use. But these methods are very computationally demanding, and lattice techniques also require careful handling of price nodes near the barrier. Kuan and Webber introduce a new approach, in which they estimate the first passage time to the barrier, and then value the option conditional on having hit the barrier. This leads to considerable improvement in performance, either less computational effort to achieve a given accuracy, or greater accuracy for a given amount of work.