A One-Factor Shifted Squared Gaussian Term Structure Model for Interest Rate Modeling

Abstract

In this article, we propose a one-factor shifted squared Gaussian model for interest rate modeling and derive closed formulas for discount bonds, bond options, caps/floors, and swaptions. Our solution is more analytically tractable than the one-factor squared Gaussian model proposed in the literature. In fact, applying the deterministic-shift extension of Brigo and Mercurio, we are able to evaluate discount bonds and interest rates options, avoiding the problems related to the use of numerical solutions. This is a major advantage in calibrating and simulating the model. In addition, we show how the proposed model can be used within the modern multiple-curve valuation framework. To appreciate the features of our model, a comparative numerical analysis is performed in a risk-neutral setting in which the Hull–White, Black–Karasinski, CIR++, and our model are analyzed and compared in terms of calibration and simulation results. Looking at the trade-off between the computation effort and the quality of the results, our model represents an interesting alternative with respect to the one-factor models widely used in financial engineering.