Pricing Rare Event Risk in Emerging Markets

This paper solves the pricing problem of an merging market debt contract in which the borrower’s economy is subject to rare event risk. Our model combines elements of a reduced form and a structural model of debt pricing. Rare event risk is modeled as a sudden event in fundamentals, and we study the role of the debt contract in providing risk sharing between the borrower and the lender. The two main frictions under consideration in our equilibrium model are limited participation of the lender through the debt contract, and heterogeneous beliefs between the borrower and the lender about the likelihood of a rare event. We solve for the rate of interest, the credit spread, the risk premium, the write-off (recovery rate) in case of default, and the dynamics of the debt contract in non-default times. We find that limited participation combined with heterogeneous beliefs has strong e®ects on the level and variability of the debt contract propertiesRare Event Risk, Emerging Markets, Exchange Economy, Heterogeneous Beliefs, Incomplete Market

Taylor Rules, McCallum Rules and the Term Structure of Interest Rates

term structure, monetary policy, Taylor rule

Financial leverage and the leverage effect: A market and firm analysis

We quantify the effect of financial leverage on stock return volatility in a dynamic general equilibrium economy with debt and equity claims. The effect of financial leverage is studied both at a market and a firm level where the firm is exposed to both idiosyncratic and market risk. In a benchmark economy with both a constant interest rate and constant price of risk, financial leverage generates little variation in stock return volatility at the market level but significant variation at the individual firm level. In an economy that generates time-variation in interest rates and the price of risk, there is significant variation in stock return volatility at the market and firm level. In such an economy, financial leverage has little effect on the dynamics of stock return volatility at the market level. Financial leverage contributes more to the dynamics of stock return volatility for a small firm.

Taylor Rules, McCallum Rules and the Term Structure of Interest Rates

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi (2002). The result echoes the policy rule used by McCallum (1994) to rationalize the empirical failure of the `expectations hypothesis' applied to the term- structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. McCallum showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. "yield-curve smoothing"), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss (1987). McCallum also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor (1993) rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term structure models studied in Duffie and Kan (1996): a stochastic volatility model and a stochastic price-of- risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by McCallum (i.e., the "McCallum Rule"). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzesi (2003)). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and McCallum Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.

Arbitrage-Free Bond Pricing with Dynamic Macroeconomic Models

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.

Arbitrage-free bond pricing with dynamic macroeconomic models

The authors examine the relationship between changes in short-term interest rates induced by monetary policy and the 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. The authors explore whether richer models of risk premiums, specifically stochastic volatility models combined with Epstein-Zin recursive utility, can account for such patterns. They study the properties of the yield curve when inflation is an exogenous process and compare this with 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 because 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. Endogenizing inflation provides a substantially better fit of the historical yield curve because 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.Bonds - Prices ; Macroeconomics

Disagreement about inflation and the yield curve

Este trabajo muestra cómo las discrepancias en torno a la inflación esperada abren una brecha entre las rentabilidades reales y nominales y elevan sus niveles y volatilidades. Se demuestra empíricamente que un incremento de estas discrepancias en una desviación estándar aumenta las rentabilidades reales y nominales y sus volatilidades, la inflación break-even y la prima de riesgo de inflación por lo menos en el 30 % de sus respectivas desviaciones estándar. Las discrepancias en torno a la inflación esperada están positivamente relacionadas con la volatilidad de sección cruzada del crecimiento del consumo y con la participación de los consumidores en los mercados de bonos, futuros sobre tipos de interés y swaps de inflación. La calibración del modelo a los datos de discrepancias en la inflación esperada, inflación y rentabilidades reproduce el impacto económicamente significativo de las discrepancias en torno a la inflación esperada sobre las curvas de rentabilidades reales y nominalesWe show theoretically that inflation disagreement drives a wedge between real and nominal yields and raises their levels and volatilities. We demonstrate empirically that an inflation disagreement increase of one standard deviation raises real and nominal yields and their volatilities, break-even inflation, and the inflation risk premium by at least 30% of their respective standard deviations. Infl ation disagreement is positively related to consumers’ cross-sectional consumption growth volatility and trading in bonds, interest rate futures, and inflation swaps. Calibrating the model to disagreement, inflation, and yield data reproduces the economically significant impact of inflation disagreement on real and nominal yield curve