Stock Price Dynamics, Dividends, and Option Prices with Volatility Feedback

In this paper, we provide a new framework for stock and options valuations by characterizing the joint dynamics of stock price, dividends, and volatility with the volatility feedback effect in continuous-time. Within our framework, we consider the properties of stock price and its dynamics with volatility feedback casting light on the excess volatility and the correlation between volatility and stock price. Most importantly, we discover a channel through which the market price of return risk, or equity risk-premium, affects option prices. One implication is that an increase in squared return volatility can be unfavorable to the holder of in-the-money call options. Finally, we illustrate the use of our framework to identifying the risk-return relation using forward-looking option data.