Structural models of default calibrated to historical default rates, recovery rates, and Sharpe ratios typically generate Baa-Aaa credit spreads that are significantly below historical values. However, this "credit spread puzzle" can be resolved if one accounts for the fact that default rates and Sharpe ratios strongly covary; both are high during recessions and low during booms. As a specific example, we investigate credit spread implications of the Campbell and Cochrane (1999) pricing kernel calibrated to equity returns and aggregate consumption data. Identifying the historical surplus consumption ratio from aggregate consumption data, we find that the implied level and time variation of spreads match historical levels well.

Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a ‘dual role’ in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits ‘unspanned stochastic volatility’ (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.

We study the extent to which credit index (CDX) options are priced consistent with S&P 500 (SPX) equity index options. We derive analytical expressions for CDX and SPX options within a structural credit‐risk model with stochastic volatility and jumps using new results for pricing compound options via multivariate affine transform analysis. The model captures many aspects of the joint dynamics of CDX and SPX options. However, it cannot reconcile the relative levels of option prices, suggesting that credit and equity markets are not fully integrated. A strategy of selling CDX volatility yields significantly higher excess returns than selling SPX volatility.

Despite regulatory efforts to promote all-to-all trading, the post–Dodd-Frank index credit default swap market remains two-tiered. Transaction costs are higher for dealer-to-client than interdealer trades, but the difference is explained by the higher, largely permanent, price impact of client trades. Most interdealer trades are liquidity motivated and executed via low-cost, low-immediacy trading protocols. Dealer-to-client trades are nonanonymous; they almost always improve upon contemporaneous executable interdealer quotes, and dealers appear to price discriminate based on the perceived price impact of trades. Our results suggest that the market structure is a consequence of the characteristics of client trades: relatively infrequent, large, and differentially informed.

We study portfolio choice when labor income and dividends are cointegrated. Economically plausible calibrations suggest young investors should take substantial short positions in the stock market. Because of cointegration the young agent's human capital effectively becomes “stock‐like.” However, for older agents with shorter times‐to‐retirement, cointegration does not have sufficient time to act, and thus their human capital becomes more “bond‐like.” Together, these effects create hump‐shaped life‐cycle portfolio holdings, consistent with empirical observation. These results hold even when asset return predictability is accounted for.

We propose an equilibrium model for defaultable bonds that are subject to contagion risk. Contagion arises because agents with “fragile beliefs” are uncertain about the underlying economic state and its probability. Estimation on sovereign European credit default swaps (CDS) data shows that agents require a time-varying risk premium for bearing state uncertainty. The model outperforms affine specifications with the same number of state variables, suggesting that there are important nonlinearities in credit spreads that are captured by our model. Contagion drives most of the variation in CDS spreads, especially before the crisis. However, economic fundamentals account for a significant fraction during the crisis.

We examine the dynamics of liquidity using a comprehensive sample of U.S. stocks in the post‐decimalization period. Motivated by a continuous‐time inventory model, we compute a high‐frequency measure of order imbalance volatility to proxy for the inventory risk faced by liquidity providers. We show that high‐frequency order imbalance volatility is an important driver of liquidity and explains the often positive time‐series relation between spread and volume for large stocks, which seems to run counter to most theoretical models. Furthermore, order imbalance volatility is priced in the cross‐section of stock returns.

Using a comprehensive sample of trades from Schedule 13D filings by activist investors, we study how measures of adverse selection respond to informed trading. We find that on days when activists accumulate shares, measures of adverse selection and of stock illiquidity are lower, even though prices are positively impacted. Two channels help explain this phenomenon: (1) activists select times of higher liquidity when they trade, and (2) activists use limit orders. We conclude that, when informed traders can select when and how to trade, standard measures of adverse selection may fail to capture the presence of informed trading.

Building on Duffie and Kan (1996) , we propose a new representation of affine models in which the state vector comprises infinitesimal maturity yields and their quadratic covariations. Because these variables possess unambiguous economic interpretations, they generate a representation that is globally identifiable . Further, this representation has more identifiable parameters than the “maximal” model of Dai and Singleton (2000) . We implement this new representation for select three‐factor models and find that model‐independent estimates for the state vector can be estimated directly from yield curve data, which present advantages for the estimation and interpretation of multifactor models.

We characterize a three‐factor model of commodity spot prices, convenience yields, and interest rates, which nests many existing specifications. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time‐varying risk premia. Both may induce mean reversion in spot prices, albeit with very different economic implications. Empirical results show strong evidence for spot‐price level dependence in convenience yields for crude oil and copper, which implies mean reversion in prices under the risk‐neutral measure. Silver, gold, and copper exhibit time variation in risk premia that implies mean reversion of prices under the physical measure.