Pricing Interest Rate Derivatives: A General Approach

Abstract

The relationship between affine stochastic processes and bond pricing equations in exponential term structure models has been well established. We connect this result to the pricing of interest rate derivatives. If the term structure model is exponential affine, then there is a linkage between the bond pricing solution and the prices of many widely traded interest rate derivative securities. Our results apply to |$m$|-factor processes with |$n$| diffusions and |$l$| jump processes. The pricing solutions require at most a single numerical integral, making the model easy to implement. We discuss many options that yield solutions using the methods of the article.