A comparison of fixed income valuation models: Pricing and econometric analysis of interest rate derivatives

This study compares several continuous-time stochastic interest rate and stochastic volatility models of interest rate derivatives, examining these models across several dimensions: different classes of models, factor structures, and pricing algorithms. We consider a broader universe of pricing models, using improved econometric and numerical methodologies. We establish several criteria for model quality that are motivated by financial theory as well as practice: realism of the assumed stochastic process for the term structure, consistency with no-arbitrage or financial market equilibrium, consistency with financial practice, parsimony, as well as computational efficiency. This helps resolve the controversies over the stochastic process for yield curve dynamics, the models that best manage and measure interest rate risk, and theories of the term structure that are supported by empirical evidence.; We perform econometric experiments at three levels: the short interest rate, bond prices, as well as interest rate derivatives. We extend CKLS (1992) to a broader class of single factor spot rate models and international interest rates. We find that a single-factor general parametric model (1FGPM) of the term structure, with non-linearity in the drift function, better captures the time series dynamics of US 30 Day T-Bill rates. Our results vary greatly across international markets. Building upon the work of Longstaff and Schwartz (1992), we perform a statistical analysis of the U.S. default-free term structure and identify at least three factors that capture 98% of the variation (level, slope, and curvature). We compare various term structure models on US Treasury bonds, ranging from the two-factor Cox-Ingersoll-Ross (2FCIR) to a multilayer perceptron neural network model (MLP-ANN). Finally, we compare various interest rate bond option pricing models, in their ability to price interest rate derivatives and manage and interest rate risk. We compare the spot rate, forward-rate, and non-parametric models (e.g., multivariate kernel estimation) and extend it to a broader factor structure. We find that no one model dominates the others under various criteria.