Analytical fixed income pricing in discrete time: A new family of models

Abstract

This paper proposes a large class of discrete-time models for interest rates, with flexible distributions on innovations and multiple factors, filling two key gaps in the literature. First, the models are “affine”, and as a result, closed-form pricing for bonds and analytical representations for more general fixed-income products can be obtained. This is reminiscent of the continuous-time models studied in Duffie et al. (2003) and the discrete-time GARCH models for assets introduced by Heston and Nandi (2000). Secondly, the models allow for control of the lower bound of the interest rate, permitting bounded negative rates. This second contribution is absent even from the popular continuous-time literature. As an application, we study the properties and interpretation of our main proposal, a Gaussian-based model with a non-central Chi-square distribution. The model is estimated via maximum likelihood on daily time series of US interest rates for various maturities and monthly interest rates from the G7 countries. The empirical analysis confirms the superiority of our model in terms of likelihood, AIC, and BIC values compared to two benchmarks, an autoregressive model as a discrete-time version of the Vasicek model, and the popular CIR model. Our model also provides additional flexibility in accommodating the yield curve, with massive potential for richer structures while maintaining the key benefits.