Ivan Shaliastovich

AN EQUILIBRIUM GUIDE TO DESIGNING AFFINE PRICING MODELS

The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out-of-the-money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options.

Learning and Asset-price Jumps

We develop a general equilibrium model in which income and dividends are smooth, but asset prices are subject to large moves (jumps). A prominent feature of the model is that the optimal decision of investors to learn the unobserved state triggers large asset-price jumps. We show that the learning choice is critically determined by preference parameters and the conditional volatility of income process. An important prediction of the model is that income volatility predicts future jumps, while the variation in the level of income does not. We find that indeed in the data large moves in returns are predicted by consumption volatility, but not by the changes in the consumption level. We show that the model can quantitatively capture these novel features of the data.

Learning, confidence, and option prices

The option-market evidence suggests that investors are concerned with large downward moves in equity prices, which occur once every one to two years in the data. This evidence is puzzling because there are no concurrent jumps in macroeconomic fundamentals. I estimate a confidence-risk model where agents use a constant gain specification to learn about the unobserved expected growth from the cross-section of signals. While consumption shocks are Gaussian, investors’ uncertainty (confidence measure) is subject to jumps, which endogenously trigger jump risks in equity and option markets. The model provides a good fit to macroeconomic, equity, option, and forecast data.

Volatility-of-Volatility Risk

We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility measures, identified model-free from options data as the VIX and VVIX indices, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average, and more negative for strategies more exposed to volatility and volatility-of-volatility risks. Volatility and volatility of volatility significantly and negatively predict future delta-hedged option payoffs. The evidence is consistent with a no-arbitrage model featuring time-varying volatility and volatility-of-volatility factors, which are negatively priced by investors.

Risk Adjustment and the Temporal Resolution of Uncertainty: Evidence from Options Markets

Risk-neutral probabilities, observable from option prices, combine objective probabilities and risk adjustments across economic states. We consider a recursive-utility framework to separately identify objective probabilities and risk adjustments using only observed market prices. We find that a preference for early resolution of uncertainty plays a key role in generating sizeable risk premia to explain the cross-section of risk-neutral and objective probabilities in the data. Failure to incorporate a preference for the timing of the resolution of uncertainty (e.g., expected utility models) can significantly overstate the implied probability of, and understate risk compensations for, adverse economic states.

Government Policy Approval and Exchange Rates

Measures of U.S. government policy approval, such as U.S. Presidential or Congressional ratings, are strongly related to persistent fluctuations in the dollar exchange rates. Contemporaneous correlations between approval ratings and the dollar value reach 50% against the advanced economy currencies, in real and nominal terms, in levels and multi-year changes. High approval ratings further forecast a decline in the dollar risk premium, a persistent increase in economic growth, and a reduction in future economic volatility several years in the future. We provide an illustrative economic model to interpret our empirical evidence. In the model, policy valuations are forward-looking and reflect net contributions of policy to economic growth. Policy valuations (approvals) increase at times of high policy-related growth and low policy-related uncertainty, which are the times of a strong dollar and low dollar risk premium.

Macroeconomic Bond Risks at the Zero Lower Bound

Close-to-zero interest rates challenge standard economic models in which zero lower bound (ZLB) is absent. We estimate a recursive utility model which features time-varying latent expected real growth, expected inflation, and stochastic inflation volatility. Using an approximate solution to bond prices, we show that the ZLB model successfully captures interest rates in a ZLB period, without a deterioration in fit to rates in normal times. Incorporating ZLB lowers the estimates of expected inflation and increases inflation volatility. It leads to large, negative and volatile shadow rates, large and volatile shadow risk premia, and small and volatile lift-off probabilities.

Volatility Risk Pass-Through

We produce novel empirical evidence on the relevance of output volatility (vol) shocks for both currency and international quantity dynamics. Focusing on G-17 countries, we document that: (1) consumption and output vols are imperfectly correlated within countries; (2) across countries, consumption vol is more correlated than output vol; (3) the pass-through of relative output vol shocks onto relative consumption vol is significant, especially for small countries; and (4) consumption differentials vol and exchange rate vol are disconnected. We rationalize these findings in a frictionless model with multiple goods and recursive preferences featuring a novel and rich risk-sharing of vol shocks.