Quantile Curves and the VRP

Cross-Section of Option Returns and the Volatility Risk Premium

AuthorsSimon Fritzsch; Felix Irresberger; Gregor Weiß

Paper linkhttps://papers.ssrn.com/sol3/papers.cfm?abstract_id=3864131

The strategy focuses on US equity American options using data from CRSP and the OptionMetrics IvyDB US database. It restricts the sample to options with one month to expiration and applies several filters, excluding cases where the ask price is below the bid, the bid equals zero, the bid–ask spread is narrower than the minimum tick size, or arbitrage bounds are violated. Options are further limited to a moneyness range between 0.5 and 1.5. The key inputs are implied volatility, moneyness, and realized volatility, with the latter calculated as the standard deviation of daily stock returns over the previous twelve months. The first step of the strategy is to construct the conditional quantile function of implied volatility given realized volatility and moneyness, which is estimated by minimizing the check-loss of the residuals using the “leveraging” machine learning technique introduced by Meir and Rätsch (2003). Based on this quantile curve, decile portfolios are formed, and the trading rule is to go long delta-hedged call options in the highest decile and short delta-hedged call options in the lowest decile. The positions are held until maturity, portfolios are equally weighted, and rebalancing occurs monthly.

The economic rationale behind the approach is that traditional sorts based on the difference between realized and implied volatilities unintentionally create portfolios that are systematically unbalanced, for instance by being long high-realized-volatility options and short low-realized-volatility ones. The quantile curve method addresses this issue by controlling directly for realized volatility and moneyness, ensuring more balanced portfolio construction and eliminating biases caused by structural differences in volatility or option characteristics. This method also has several advantages: it does not require assuming a specific functional form for the relationship between implied and realized volatility, it helps avoid the issue of empty portfolios, and it allows the inclusion of additional conditioning variables if needed. Finally, once the quantile curves are estimated, the strategy is straightforward to implement on a recurring monthly basis.