Pricing Interest Rate Derivatives with Multilinear Interpolations and Transition Densities

Abstract

We present a general and flexible numerical procedure for pricing European interest-rate derivatives within multifactor affine term structure models by means of piecewise multilinear interpolations. Our procedure relies to the maximum extent on the true density of the state process and solves the pricing problem in quasi-closed form. Then, we show how to generalize our approach for pricing American-style options. As an illustration, we price European interest-rate swaptions and Eurodollar futures options, which cannot be analytically evaluated. We use nine affine models and show that our approach converges rapidly and competes well against Monte Carlo simulation. We also demonstrate that our approach remains well-behaved for pricing deeply out-of-the money interest-rate derivatives.