Research Papers

The Factor Structure in Equity Options, (Forthcoming RFS)

with P. Christoffersen and K. Jacobs

Equity options display a strong factor structure. The first principal components of the equity volatility levels, skews, and term structures explain a substantial fraction of the cross-sectional variation. Furthermore, these principal components are highly correlated with the S&P500 index option volatility, skew, and term structure respectively. We develop an equity option valuation model that captures this factor structure. The model predicts that firms with higher market betas have higher implied volatilities, steeper moneyness slopes, and a term structure that co-varies more with the market. The model provides a good fit and the equity option data support the model’s cross-sectional implications.

A pdf version of the paper is available here.


Beta Risk in the Cross-Section of Equities, (R&R RFS)

with A. Boloorforoosh, P. Christoffersen, and C. Gouriéroux

We develop a bivariate stochastic volatility model that allows for dynamic market exposure. The expected return on a stock depends on beta’s co-movement with the stochastic discount factor and deviates from the standard security market line when beta risk is priced. When estimating the model on returns and options for a large number of firms we find that allowing for beta risk helps explain the expected returns on low and high beta stocks that are challenging for standard factor models. Overall, we find strong evidence that accounting for beta risk results in better model fit.

A pdf version of the paper is available here.


A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth, (R&R JFQA)

with K. Jacobs

We develop a tractable dynamic model of an index option market maker with limited capital and characterize how option prices depend on inventory risk and market maker wealth. The risk averse market maker absorbs positive demand by end users and requires a more negative variance risk premium when she incurs losses. The model is parsimonious and nests existing reduced-form stochastic-volatility models. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by existing stochastic-volatility models are strongly rejected in favor of the model with a market maker.

A pdf version of the paper is available here.


Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk

with P. Christoffersen, K. Jacobs, and M. Karoui

We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. The price of co-skewness risk corresponds to the market variance risk premium, and the price of co-kurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models’ performance compared to regression-based estimates.

A pdf version of the paper is available here.


When the Options Market Disagrees

with R. Goyenko and G. Grass

We construct a new measure of investor disagreement from signed equity options trading volumes. Options disagreement negatively predicts stock returns over various horizons. The high disagreement stock portfolio underperforms the low disagreement portfolio by 5.7% per year after standard risk adjustments. Options disagreement increases around news releases but its predictive power for stock returns does not depend on the news content. Higher short-selling costs in the stock market result in higher disagreement and increase its impact on expected stock returns. Overall, our results are consistent with differences of opinion theories where investors “agree to disagree” in the options market.

A pdf version of the paper is available here.