Lattice methods for no-arbitrage pricing of interest rate securities

Abstract

We explore calibration of single factor no-arbitrage short rate models to yield and volatility information. We note that the calculation of Arrow-Debreu prices for interest rate securities is analogous to solving the Kolmogorov Forward Equation. This insight allows us to implement implicit methods which exhibit more rapid convergence than explicit methods. We develop an algorithm for calibrating a model to match both yield and volatility curves which is general across single factor short rate models and also across finite difference techniques. Numerical examples confirm that our approach vastly improves computation times for derivative pricing.