Model Uncertainty and Liquidity

Extreme market outcomes are often followed by a lack of liquidity and a lack of trade. This market collapse seems particularly acute for markets where traders rely heavily on a specific empirical model such as in derivative markets. Asset pricing and trading, in these cases, are intrinsically model dependent. Moreover, the observed behavior of traders and institutions that places a large emphasis on 'worst-case scenarios'' through the use of 'stress testing'' and 'value-at-risk'' seems different than Savage rationality (expected utility) would suggest. In this paper we capture model-uncertainty explicitly using an Epstein-Wang (1994) uncertainty-averse utility function with an ambiguous underlying asset-returns distribution. To explore the connection of uncertainty with liquidity, we specify a simple market where a monopolist financial intermediary makes a market for a propriety derivative security. The market-maker chooses bid and ask prices for the derivative, then, conditional on trade in this market, chooses an optimal portfolio and consumption. We explore how uncertainty can increase the bid-ask spread and, hence, reduces liquidity. In addition, 'hedge portfolios'' for the market-maker, an important component to understanding spreads, can look very different from those implied by a model without Knightian uncertainty. Our infinite-horizon example produces short, dramatic decreases in liquidity even though the underlying environment is stationary.

Generalized Disappointment Aversion and Asset Prices

We provide an axiomatic model of preferences over atemporal risks that generalizes Gul (1991) A Theory of Disappointment Aversion' by allowing risk aversion to be first order' at locations in the state space that do not correspond to certainty. Since the lotteries being valued by an agent in an asset-pricing context are not typically local to certainty, our generalization, when embedded in a dynamic recursive utility model, has important quantitative implications for financial markets. We show that the state-price process, or asset-pricing kernel, in a Lucas-tree economy in which the representative agent has generalized disappointment aversion preferences is consistent with the pricing kernel that resolves the equity-premium puzzle. We also demonstrate that a small amount of conditional heteroskedasticity in the endowment-growth process is necessary to generate these favorable results. In addition, we show that risk aversion in our model can be both state-dependent and counter-cyclical, which empirical research has demonstrated is necessary for explaining observed asset-pricing behavior.

Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology

We model equilibrium spot and futures oil prices in a general equilibrium production economy. In our model production of the consumption good requires two inputs: the consumption good and a commodity, e.g., Oil. Oil is produced by wells whose flow rate is costly to adjust. Investment in new Oil wells is costly and irreversible. As a result in equilibrium, investment in Oil wells is infrequent and lumpy. Even though the state of the economy is fully described by a one-factor Markov process, the spot oil price is not Markov (in itself). Rather it is best described as a regime-switching process, the regime being an investment `proximity' indicator. The resulting equilibrium oil price exhibits mean-reversion and heteroscedasticity. Further, the risk premium for exposure to commodity risk is time-varying, positive in the far-from-investment regime but negative in the near-investment regime. Further, our model captures many of the stylized facts of oil futures prices, such as backwardation and the `Samuelson effect.' The futures curve exhibits backwardation as a result of a convenience yield, which arises endogenously. We estimate our model using the Simulated Method of Moments with economic aggregate data and crude oil futures prices. The model successfully captures the first two moments of the futures curves, the average non-durable consumption-output ratio, the average oil consumption-output and the average real interest rate. The estimation results suggest the presence of convex adjustment costs for the investment in new oil wells. We also propose and test a linear approximation of the equilibrium regime-shifting dynamics implied by our model, and test its empirical implication for time-varying risk-premia.

Character Sequence Models for ColorfulWords

We present a neural network architecture to predict a point in color space from the sequence of characters in the color's name. Using large scale color--name pairs obtained from an online color design forum, we evaluate our model on a "color Turing test" and find that, given a name, the colors predicted by our model are preferred by annotators to color names created by humans. Our datasets and demo system are available online at colorlab.us

Model Uncertainty and Liquidity

We investigate the dynamic portfolio problem of a market-maker for a derivative security whose preferences exhibit uncertainty aversion (Knightian uncertainty). The Choquet-expected utility implied by such preference is used to capture the feature that the trader is uncertain about which model should be used. The prices that emerge from the model are similar to standard models and have the feature that as uncertainty is removed, the derivative prices converge to standard prices. However, the optimal changes in the agent's portfolio that results from the option position are quite different than the standard hedge position. It is this feature that links uncertainty with market liquidity.

"Recursive Preferences,"

We summarize the class of recursive preferences. These preferences fit naturally with recursive solution methods and hold the promise of generating new insights into familiar problems. Portfolio choice is used as an example

"Recursive Preferences,"

We summarize the class of recursive preferences. These preferences fit naturally with recursive solution methods and hold the promise of generating new insights into familiar problems. Portfolio choice is used as an example