We nest multiple volatility components, fat tails, and a U-shaped pricing kernel in a single option model and compare their contribution in describing returns and option data. All three features lead to statistically significant model improvements. A U-shaped pricing kernel is economically most important and improves option fit by 17%, on average, and more so for two-factor models. A second volatility component improves the option fit by 9%, on average. Fat tails improve option fit by just over 4%, on average, but more so when a U-shaped pricing kernel is applied. Overall, these three model features are complements rather than substitutes: the importance of one feature increases in conjunction with the others.

The Black-Scholes-Merton option valuation method involves deriving and solving a partial differential equation (PDE). But this method can generate multiple values for an option. We provide new solutions for the Cox-Ingersoll-Ross (CIR) term structure model, the constant elasticity of variance (CEV) model, and the Heston stochastic volatility model. Multiple solutions reflect asset pricing bubbles, dominated investments, and (possibly infeasible) arbitrages. We provide conditions to rule out bubbles on underlying prices. If they are not satisfied, put-call parity might not hold, American calls have no optimal exercise policy, and lookback calls have infinite value. We clarify a longstanding conjecture of Cox, Ingersoll, and Ross.

This paper studies seasonal predictability in the cross section of international stock returns. Stocks that outperform the domestic market in a particular month continue to outperform the domestic market in that same calendar month for up to 5 years. The pattern appears in Canada, Japan, and 12 European countries. Global trading strategies based on seasonal predictability outperform similar nonseasonal strategies by over 1% per month. Abnormal seasonal returns remain after controlling for size, beta, and value, using global or local risk factors. In addition, the strategies are not highly correlated across countries. This suggests they do not reflect return premiums for systematic global risk.

We examine the influence of industrial structure on the cross-sectional volatility and correlation structure of country index returns for 12 European countries between 1978 and 1992. We find that industrial structure explains very little of the cross-sectional difference in country return volatility, and that the low correlation between country indices is almost completely due to country-specific sources of return variation. Diversification across countries within an industry is a much more effective tool for risk reduction than industry diversification within a country.

We develop a GARCH option model with a new pricing kernel allowing for a variance premium. While the pricing kernel is monotonic in the stock return and in variance, its projection onto the stock return is nonmonotonic. A negative variance premium makes it U shaped. We present new semiparametric evidence to confirm this U-shaped relationship between the risk-neutral and physical probability densities. The new pricing kernel substantially improves our ability to reconcile the time-series properties of stock returns with the cross-section of option prices. It provides a unified explanation for the implied volatility puzzle, the overreaction of long-term options to changes in short-term variance, and the fat tails of the risk-neutral return distribution relative to the physical distribution. The Author 2013. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.

We develop a model-free measure of the variance premium by constructing option portfolios whose returns are highly correlated with realized stock variance. This effectively decomposes returns into realized variance minus implied variance. We apply this decomposition to document a novel quarterly cross-sectional continuation pattern in both realized variance and implied variance of individual stocks. Implied variance underanticipates the seasonality of realized variance, so options that performed well at quarterly lags continue to earn high returns in the future. Quarterly periodicity in realized stock variance only occurs on days with analyst earning revisions, suggesting an informational channel for this pattern.

Motivated by the literature on investment flows and optimal trading, we examine intraday predictability in the cross‐section of stock returns. We find a striking pattern of return continuation at half‐hour intervals that are exact multiples of a trading day, and this effect lasts for at least 40 trading days. Volume, order imbalance, volatility, and bid‐ask spreads exhibit similar patterns, but do not explain the return patterns. We also show that short‐term return reversal is driven by temporary liquidity imbalances lasting less than an hour and bid‐ask bounce. Timing trades can reduce execution costs by the equivalent of the effective spread.

This paper investigates the performance of option investments across different stocks by computing monthly returns on at‐the‐money straddles on individual equities. We find that options with high historical returns continue to significantly outperform options with low historical returns over horizons ranging from 6 to 36 months. This phenomenon is robust to including out‐of‐the‐money options or delta‐hedging the returns. Unlike stock momentum, option return continuation is not followed by long‐run reversal. Significant returns remain after factor risk adjustment and after controlling for implied volatility and other characteristics. Across stocks, trading costs are unrelated to the magnitude of momentum profits.