Equities

Forecasting the Distribution of Option Returns

Topics - Equities Volatility

${ numberSection } ${ text }
Forecasting the Distribution of Option Returns

We propose a method for constructing conditional option return distributions. In our model, uncertainty about the future option return has two sources: Changes in the position and shape of the implied volatility surface that shift option values (holding moneyness and maturity fixed), and changes in the underlying price which alter an option's location on the surface and thus its value (holding the surface fixed). We estimate a joint time series model of the spot price and volatility surface and use this to construct an ex ante characterization of the option return distribution via bootstrap. Our "ORB" (option return bootstrap) model accurately forecasts means, variances, and extreme quantiles of S&P 500 index conditional option return distributions across a wide range of strikes and maturities. We illustrate the value of our approach for practical economic problems such as risk management and portfolio choice. We also use the model to illustrate the risk and return tradeoff throughout the options surface conditional on being in a high or low risk state of the world. Comparing against our less structured but more accurate model predictions helps identify misspecification of risks and risk pricing in traditional no-arbitrage option models with stochastic volatility and jumps.

AQR Capital Management, LLC, (“AQR”) provide links to third-party websites only as a convenience, and the inclusion of such links does not imply any endorsement, approval, investigation, verification or monitoring by us of any content or information contained within or accessible from the linked sites. If you choose to visit the linked sites, you do so at your own risk, and you will be subject to such sites' terms of use and privacy policies, over which AQR.com has no control. In no event will AQR be responsible for any information or content within the linked sites or your use of the linked sites.

 

The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees. This information is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein. Past performance is not a guarantee of future results.

 

Hypothetical performance results have many inherent limitations, some of which, but not all, are described herein. Hypothetical performance results are presented for illustrative purposes only.

 

Diversification does not eliminate the risk of experiencing investment loss.

 

Certain publications may have been written prior to the author being an employee of AQR.

This material is intended for informational purposes only and should not be construed as legal or tax advice, nor is it intended to replace the advice of a qualified attorney or tax advisor.