Options and Risk

Abstract

We propose a parsimonious general equilibrium extension of the Black-Scholes economy that helps clarify how options' prices, expected returns, risk exposure, and optimal exercise policies respond to variations in the risk exposure of the underlying asset. The model allows one to separate the effects from changes in idiosyncratic versus systematic risk. Among the new insights we establish are that i) call prices typically respond negatively to increases in systematic risk, ii) the magnitude of call and put options' expected returns are monotonically decreasing in idiosyncratic risk, and iii) the optimal exercise date of an American put can be pushed backwards in time in response to an increase in systematic risk---decreasing the value of waiting. The effects of a change in risk on options are generally ambiguous because it affects their prices through two key channels---the volatility channel and the price channel---and a change in systematic risk causes a repricing of the underlying asset that may dominate the volatility channel. The comparative statics are robust to the presence of stochastic volatility, and thus yield internally consistent implications not only for the cross-section of options but also for the time-series of a particular option.