Forward rate dynamics are modeled as a random field. In contrast to multifactor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk-neutral measure is obtained. Forward risk-adjusted measures are identified and used to price a bond option when the forward volatility structure depends on the square root of the current spot rate. Several classes of tractable random field models are presented.

Forward rate dynamics are modeled as a random field. In contrast to multifactor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk-neutral measure is obtained. Forward risk-adjusted measures are identified and used to price a bond option when the forward volatility structure depends on the square root of the current spot rate. Several classes of tractable random field models are presented.

We investigate the joint optimal risk management and capital structure decisions of banks when they use contingent-convertible (CoCo) futures contracts to hedge financial-sector risk. In spite of banks choosing significantly higher leverage ratios, their default probabilities drop appreciably while their equity values increase, allowing banks to compete more favorably with the shadow-banking system. Banks’ value-maximizing decision to hedge financial-sector risk unintentionally leads to an economy with extremely low aggregate bank default rates across all future states of nature. Thus, CoCo futures offer a powerful microprudential and macroprudential policy tool. That banks choose not to hedge financial-sector risk in practice is consistent with managers internalizing bank bailouts.

The 1987 market crash was associated with a dramatic and permanent steepening of the implied volatility curve for equity index options, despite minimal changes in aggregate consumption. We explain these events within a general equilibrium framework in which expected endowment growth and economic uncertainty are subject to rare jumps. The arrival of a jump triggers the updating of agents' beliefs about the likelihood of future jumps, which produces a market crash and a permanent shift in option prices. Consumption and dividends remain smooth, and the model is consistent with salient features of individual stock options, equity returns, and interest rates.

[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.]

Reduced-form models of default that attribute a large fraction of credit spreads to compensation for credit-event risk typically preclude the most plausible economic justification for such risk to be priced, namely, a contemporaneous drop in the market portfolio. When this "contagion" channel is introduced within a general equilibrium framework for an economy comprising a large number of firms, credit-event risk premia have an upper bound of a few basis points, and are dwarfed by the contagion premium. We provide empirical evidence that indicates credit-event risk premia are less than 1 bp, but contagion risk premia are significant.

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.

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 term structure models assume bond markets are complete, that is, that all fixed income derivatives can be perfectly replicated using solely bonds. How ever, we find that, in practice, swap rates have limited explanatory power for returns on at‐the‐money straddles—portfolios mainly exposed to volatility risk. We term this empirical feature unspanned stochastic volatility (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USV models, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.

Most structural models of default preclude the firm from altering its capital structure. In practice, firms adjust outstanding debt levels in response to changes in firm value, thus generating mean‐reverting leverage ratios. We propose a structural model of default with stochastic interest rates that captures this mean reversion. Our model generates credit spreads that are larger for low‐leverage firms, and less sensitive to changes in firm value, both of which are more consistent with empirical findings than predictions of extant models. Further, the term structure of credit spreads can be upward sloping for speculative‐grade debt, consistent with recent empirical findings.