We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed‐form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.

With dual trading, brokers trade both for their customers and for their own account. We study dual trading and find that customers who are less likely to be informed have higher expected profits with dual trading while customers who are more likely to be informed have higher expected profits without dual trading. We also examine the effects of frontrunning. We test the major empirical implications of our model. Consistent with the model, dual traders earn higher profits than non-dual traders, and customers of dual-trading brokers do better than customers of non-dual-trading brokers.

With dual trading, brokers trade both for their customers and for their own account. We study dual trading and find that customers who are less likely to be informed have higher expected profits with dual trading while customers who are more likely to be informed have higher expected profits without dual trading. We also examine the effects of frontrunning. We test the major empirical implications of our model. Consistent with the model, dual traders earn higher profits than non‐dual traders, and customers of dual‐trading brokers do better than customers of non‐dual‐trading brokers.

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.

We develop a two‐factor general equilibrium model of the term structure. The factors are the short‐term interest rate and the volatility of the short‐term interest rate. We derive closed‐form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed‐form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross‐sectional restrictions imposed by the model. The tests support the two‐factor model.

This paper studies the costs of applying single-factor exercise strategies to American swap options when the term structure is actually driven by multiple factors. Using a multifactor string market model of the term structure, we find that even when single-factor models are recalibrated to match the market at every exercise date, the exercise strategies they imply can be suboptimal. Based on estimates of notional amounts outstanding, the total present value costs of following single-factor strategies could be several billion dollars. These results illustrate the importance of using well-specified term structure models.

We solve a model with two i.i.d. Lucas trees. Although the corresponding one-tree model produces a constant price-dividend ratio and i.i.d. returns, the two-tree model produces interesting asset-pricing dynamics. Investors want to rebalance their portfolios after any change in value. Because the size of the trees is fixed, prices must adjust to offset this desire. As a result, expected returns, excess returns, and return volatility all vary through time. Returns display serial correlation and are predictable from price-dividend ratios. Return volatility differs from cash-flow volatility, and return shocks can occur without news about cash flows.

Many firms have stockholders who face severe restrictions on their ability to sell their shares and diversify the risk of their personal wealth. We study the costs of these liquidity restrictions on stockholders using a continuous-time portfolio choice framework. These restrictions have major effects on the optimal investment and consumption strategies because of the need to hedge the illiquid stock position and smooth consumption in anticipation of the eventual lapse of the restrictions. These results provide a number of important insights about the effects of illiquidity in financial markets.

We conduct an analysis of the risk and return characteristics of a number of widely used fixed-income arbitrage strategies. We find that the strategies requiring more “intellectual capital” to implement tend to produce significant alphas after controlling for bond and equity market risk factors. These positive alphas remain significant even after taking into account typical hedge fund fees. In contrast with other hedge fund strategies, many of the fixed-income arbitrage strategies produce positively skewed returns. These results suggest that there may be more economic substance to fixed-income arbitrage than simply “picking up nickels in front of a steamroller.”

We study corporate bond default rates using an extensive new data set spanning the 1866–2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873–1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.