Arbitrage-Free Bond Pricing with Dynamic Macroeconomic Models

Abstract

We examine the relationship between monetary-policy-induced changes in short interest rates and yields on long-maturity default-free bonds. The volatility of the long end of the term structure and its relationship with monetary policy are puzzling from the perspective of simple structural macroeconomic models. We explore whether richer models of risk premiums, specifically stochastic volatility models combined with Epstein-Zin recursive utility, can account for such patterns. We study the properties of the yield curve when inflation is an exogenous process and compare this to the yield curve when inflation is endogenous and determined through an interest-rate/Taylor rule. When inflation is exogenous, it is difficult to match the shape of the historical average yield curve. Capturing its upward slope is especially difficult as the nominal pricing kernel with exogenous inflation does not exhibit any negative autocorrelation-a necessary condition for an upward sloping yield curve as shown in Backus and Zin (1994). Endogenizing inflation provides a substantially better fit of the historical yield curve as the Taylor rule provides additional flexibility in introducing negative autocorrelation into the nominal pricing kernel. Additionally, endogenous inflation provides for a flatter term structure of yield volatilities which better fits historical bond data.

The Yield Curve and Financial Risk Premia

“…They do not resemble a feedback rule from a "nominal anchor" where the interest rate instrument reacts to observable current and lagged endogenous variables characterizing the state of the economy (McCallum 1981). Recently, Gallmeyer et al (2005) and Gallmeyer et al (2007) have combined equilibrium short-rate paths with different monetary reaction functions. 45 Therefore, it is inappropriate to compare such an interest-rate characterization with a Taylor rule since the former is not an instrument rule per se but already an equilibrium solution for short-term interest rates.…”

On the Need for a New Approach to Analyzing Monetary Policy

“…Since the early contribution by McCallum (1994), a large literature has studied interest rates in such economies. Examples include the work of Wachter (2006), Bansal and Shaliastovich (2007), Gallmeyer, Hollifield, Palomino, and Zin (2007), Piazzesi and Schneider (2007).…”

“…Examples include Wachter (2006), Bansal and Shaliastovich (2007), Gallmeyer, Hollifield, Palomino, and Zin (2007), Piazzesi and Schneider (2007). Our model draws most heavily from the work of Gallmeyer, Hollifield, and Zin (2005).…”

Immunization of Fixed-Income Portfolios Using an Exponential Parametric Model

“…To this end, authors such as Ang et al (2007), Bernanke et al (2004), Gallmeyer et al (2007), BeKaert et al (2005), to name a few, have recently tried to describe this relation, although in the framework of dynamic term structure models. Other extensions would be: empirically testing the robustness of the immunization strategies in and out of sample, using credit restrictions and second order optimal conditions, that is, to use the convexity of the portfolio to the maximum to carry out a hedging operation that surpasses the limit of portfolio protection.…”