This paper analyzes the role of jumps in continuous‐time short rate models. I first develop a test to detect jump‐induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparametric jump‐diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps. Jumps generally have a minor impact on yields, but they are important for pricing interest rate options.

[Previous research concludes that options are mispriced based on the high average returns, CAPM alphas, and Sharpé ratios of various put selling strategies. One criticism of these conclusions is that these benchmarks are ill suited to handle the extreme statistical nature of option returns generated by nonlinear payoffs. We propose an alternative way to evaluate the statistical significance of option returns by comparing historical statistics to those generated by option pricing models. The most puzzling finding in the existing literature, the large returns to writing out-of-the-money puts, is not inconsistent (i.e.,is statistically insignificant) relative to the Black-Scholes model or the Heston stochastic volatility model due to the extreme sampling uncertainty associated with put returns. This sampling problem can largely be alleviated by analyzing market-neutral portfolios such as straddles or deltahedged returns. The returns on these portfolios can be explained by jump risk premiums and estimation risk.]

Recent evidence suggests that younger people update beliefs in response to aggregate shocks more than older people. We embed this generational learning bias in an equilibrium model in which agents have recursive preferences and are uncertain about exogenous aggregate dynamics. The departure from rational expectations is statistically modest, but generates high average risk premiums varying at generational frequencies, a positive relation between past returns and agents' future return forecasts, and substantial and persistent over-and undervaluation. Consistent with the model, the price-dividend ratio is empirically more sensitive to macroeconomic shocks when the fraction of young in the population is higher.

[This paper provides an optimal filtering methodology in discretely observed continuoustime jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filter's performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns.]

This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filter's performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns.

This paper characterizes U.S. consumption dynamics from the perspective of a Bayesian agent who does not know the underlying model structure but learns over time from macroeconomic data. Realistic, high‐dimensional macroeconomic learning problems, which entail parameter, model, and state learning, generate substantially different subjective beliefs about consumption dynamics compared to the standard, full‐information rational expectations benchmark. Beliefs about long‐run dynamics are volatile, with counter‐cyclical conditional volatility, and drift over time. Embedding these beliefs in a standard asset pricing model significantly improves the model's ability to match the stylized facts, as well as the sample path of the market price‐dividend ratio.

Previous research concludes that options are mispriced based on the high average returns, CAPM alphas, and Sharpe ratios of various put selling strategies. One criticism of these conclusions is that these benchmarks are ill-suited to handle the extreme statistical nature of option returns generated by nonlinear payoffs. We propose an alternative way to evaluate the statistical significance of option returns by comparing historical statistics to those generated by option pricing models. The most puzzling finding in the existing literature, the large returns to writing out-of-the-money puts, is not inconsistent (i.e., is statistically insignificant) relative to the Black-Scholes model or the Heston stochastic volatility model due to the extreme sampling uncertainty associated with put returns. This sampling problem can largely be alleviated by analyzing market-neutral portfolios such as straddles or delta-hedged returns. The returns on these portfolios can be explained by jump risk premia and estimation risk.

Parameter learning strongly amplifies the impact of macroeconomic shocks on marginal utility when the representative agent has a preference for early resolution of uncertainty. This occurs as rational belief updating generates subjective long-run consumption risks. We consider general equilibrium models with unknown parameters governing either long-run economic growth, rare events, or model selection. Overall, parameter learning generates long-lasting, quantitatively significant additional macroeconomic risks that help explain standard asset pricing puzzles.

Interest rate swap pricing theory traditionally views swaps as a portfolio of forward contracts with net swap payments discounted at LIBOR rates. In practice, the use of marking‐to‐market and collateralization questions this view as they introduce intermediate cash flows and alter credit characteristics. We provide a swap valuation theory under marking‐to‐market and costly collateral and examine the theory's empirical implications. We find evidence consistent with costly collateral using two different approaches; the first uses single‐factor models and Eurodollar futures prices, and the second uses a formal term structure model and Treasury/swap data.

This paper finds statistically and economically significant out‐of‐sample portfolio benefits for an investor who uses models of return predictability when forming optimal portfolios. Investors must account for estimation risk, and incorporate an ensemble of important features, including time‐varying volatility, and time‐varying expected returns driven by payout yield measures that include share repurchase and issuance. Prior research documents a lack of benefits to return predictability, and our results suggest that this is largely due to omitting time‐varying volatility and estimation risk. We also document the sequential process of investors learning about parameters, state variables, and models as new data arrive.