Indifference Prices, Implied Volatilities and Implied Sharpe Ratios

Abstract: We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, we derive an explicit approximation for the buyer's and seller's indifference prices. Additionally, we translate indifference prices into an explicit approximation of implied volatility surfaces. We also introduce the concept of an "implied Sharpe ratio" and derive explicit approximations for this quantity. Like implied volatility, the implied Sharpe ratio can be viewed as a measure of an option's value. The advantage of the implied Sharpe ratio is that, unlike implied volatility, it considers an investor's preferences and alternative investment possibilities.