Dynamic equilibrium models based on present value computation not only imply that returns are predictable but also generate particular short-term patterns of predictability in asset returns. I take advantage of this to construct a set of tests of equilibrium generated predictability (EGP). I apply the tests to document two puzzles: First, option-implied or realized measures of volatility ought to predict returns but do not; and second, the variance risk premium (VRP) predicts returns but only at long horizons. VRP fails the tests of EGP as the term structure of predictable variation is inconsistent with an equilibrium interpretation.

High expected inflation is known to predict low future real growth. We show that, relative to nondurable goods sectors of the economy, such predictability is significantly more pronounced in durable sectors. Consistent with this macroeconomic evidence, the equity returns of durable goods-producing firms have a larger negative exposure to expected inflation risks. We estimate a two-good recursive utility model that features persistent growth fluctuations and inflation nonneutrality for durable and nondurable consumption. Our model can quantitatively account for the levels and volatilities of bond and equity prices, and correlations of equity returns with bond returns and with expected inflation.

This paper examines the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data. The paper introduces a model with discontinuous correlated jumps in stock prices and stock price volatility, and with state‐dependent arrival intensity. We discuss how to perform likelihood‐based inference based upon joint options/returns data and present estimates of risk premiums for jump and volatility risks. The paper finds that while complex jump specifications add little explanatory power in fitting options data, these models fare better in fitting options and returns data simultaneously.

We study returns on over-the-counter stocks and find that these returns are extremely negative on average. The distribution of OTC stock returns is highly positively skewed: while many of the stocks in our sample become worthless, a few do extremely well. We investigate whether this negative return premium can be rationalized by investors׳ preference for positively skewed payoffs. We show that the equilibrium model of Barberis and Huang (2008) provides a plausible explanation for the negative returns. We also show that OTC stocks that once traded on the regular exchanges perform much better than stocks that originate in the OTC markets.

We develop a tractable equilibrium pricing model to explain observed characteristics in equity returns, VIX futures, S&P 500 options, and VIX options data based on affine jump‐diffusive state dynamics and representative agents endowed with Duffie‐Epstein recursive preferences. Our calibrated model replicates consumption, dividends, and asset market data, including VIX futures returns, the average implied volatilities in SPX and VIX options, and first‐ and higher‐order moments of VIX options returns. We document a time variation in the shape of VIX‐option‐implied volatility and a time‐varying hedging relationship between VIX and SPX options that our model both captures.

This paper examines continuous‐time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood‐based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing.

We study the returns to investing in VIX futures, VIX Exchange Traded Notes (ETNs), and variance swaps. We document substantial negative return premia for these assets. For example, the constant maturity portfolio of 1-month VIX futures loses about 30% per year over our sample period (2006–2013). We investigate if these findings are consistent with dynamic equilibrium. We derive a model based on present value computation that endogenizes stock prices, the VIX index, and its associated derivative contracts. The model explains the negative return premia as well as several other stylized features of the VIX futures, ETNs, and variance swap data.

High expected inflation is known to predict low future real growth. We show that, relative to nondurable goods sectors of the economy, such predictability is significantly more pronounced in durable sectors. Consistent with this macroeconomic evidence, the equity returns of durable goods-producing firms have a larger negative exposure to expected inflation risks. We estimate a two-good recursive utility model that features persistent growth fluctuations and inflation nonneutrality for durable and nondurable consumption. Our model can quantitatively account for the levels and volatilities of bond and equity prices, and correlations of equity returns with bond returns and with expected inflation.