Stock Price Dynamics and Option Valuations under Volatility Feedback Effect

TL;DR

This paper models stock price and option dynamics considering the volatility feedback effect, showing how increased volatility impacts stock prices and deep-in-the-money options, and explaining the volatility puzzle through market risk premiums.

Contribution

It introduces a continuous-time model capturing the joint dynamics of stock prices, dividends, and volatility under the volatility feedback effect, linking market risk premiums to option prices.

Findings

Increased squared volatility reduces stock price-dividend ratio.

Higher volatility negatively impacts deep-in-the-money call options.

Ignoring time-varying dividends oversimplifies stock market dynamics.

Abstract

According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.