An Overview of Derivative Pricing in Gaussian Affine Asset Pricing Models: An Application to the KNW Model

Abstract

We present a comprehensive overview of derivative pricing in Gaussian affine asset pricing models. Gaussian affine asset pricing models are widely used in practice for pricing and scenario analysis due to their tractable pricing implications and easy estimation. This tractability is essential to efficiently evaluate portfolios of derivatives within many scenarios and time periods. We present efficient closed-form pricing formulas for the most common derivative instruments used by pension funds and insurance companies, such as interest rate swaps, swaptions, inflation-linked swaps, equity options, based on results from the literature. The pricing formulas are presented in a comprehensive computable form by utilising results based on the matrix exponential. Next, we show how some models commonly used in practice fit in the Gaussian affine framework, so that the pricing formulas can be applied to these cases. In particular, we discuss the KNW model by Koijen, Nijman and Werker (2010), which is widely used in the pension industry. Finally we discuss how our results can be applied to a time-inhomogeneous extension of the model that allows perfect calibration to the observed yield curve.