Smile dynamics -- a theory of the implied leverage effect

TL;DR

This paper develops a theoretical framework for the implied leverage effect, explaining how leverage influences stock option smile skew and its dynamics, and compares model predictions with market data revealing overestimation of leverage effects.

Contribution

It introduces a detailed theory linking leverage effect to smile skew and dynamics, and analyzes market overestimation of leverage impact on options.

Findings

Leverage effect explains skew dependence on maturity.

Option markets overestimate leverage effect, especially for long-term options.

Smile dynamics are intermediate between sticky strike and sticky delta models.

Abstract

We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence of the leverage effect is analyzed using a one-factor model. We show how this leverage correlation gives rise to a non-trivial smile dynamics, which turns out to be intermediate between the "sticky strike" and the "sticky delta" rules. Finally, we compare our result with stock option data, and find that option markets overestimate the leverage effect by a large factor, in particular for long dated options.