Research Papers

Publications and Peer Reviewed Papers

The Factor Structure in Equity Options, with P. Christoffersen and K. Jacobs

The Review of Financial Studies, Volume 31, Issue 2, February 2018, Pages 595–637.

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

The Review of Financial Studies, Conditionally Accepted.

Abstract: We develop a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure. When beta co-moves with market variance and the stochastic discount factor (SDF), beta risk is priced, and the expected return on a stock deviates from the security market line. The model predicts that low-beta stocks earn high returns because their beta co-moves positively with market variance and the SDF. The opposite is true for high-beta stocks. Estimating the model on equity and option data, we find that beta risk explains expected returns on low- and high-beta stocks, resolving the “betting against beta” anomaly.

A pdf version of the paper is available here.


A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth, with K. Jacobs

The Journal of Financial and Quantitative Analysis, Forthcoming.

Abstract:  We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

A pdf version of the paper is available here.

Working Papers

Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk, with P. Christoffersen, K. Jacobs, and M. Karoui

The Journal of Financial and Quantitative Analysis, R&R.

Abstract: 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.


The Low-Minus-High Portfolio and the Factor Zoo, with D. Andrei, and J. Cujean

Abstract: Anomalies in the cross section of returns should not be regarded as evidence against the CAPM. Regardless whether the CAPM is rejected for valid reasons or by mistake, a single long-short portfolio will always explain, together with the market, 100% of the cross-sectional variation in returns. Yet, this portfolio need not proxy for fundamental risk. We show theoretically how factors based on valuation ratios (e.g, book-to-market), or on investment rates, can be proxies for this portfolio. More generally, the empiricist can uncover an infinity of proxies for this portfolio, thus unleashing the factor zoo.

A pdf version of the paper is available here.


When the Options Market Disagrees, with R. Goyenko and G. Grass

Abstract: 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.

Work in Progress

Variance Risk Premia across Three Derivatives Markets with H. Doshi, J. Ericsson, and S. B. Seo.


The Economic Value of Modeling Volatilities-Covolatilities via Machine Learning, with V. Grégoire


A Deep Learning Approach to Option Valuation with Friction and Liquidity Measures, with P. Orlowski and J. Pilault


The Relative Pricing of Long-Run and Short-Run Betas in the Cross-Section of Stock Returns, with A. Jeanneret