We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for both the buyer's and seller's indifference price. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surface. For European claims on a non-traded asset, we establish rigorous error bounds for the indifference price approximation. 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 takes into account an investor's preferences and his alternative investment possibilities. We implement our indifference price , implied volatility and implied Sharpe ratio approximations in two examples.
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for both the buyer's and seller's indifference price. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surface. For European claims on a non-traded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.
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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 takes into account an investor's preferences and his alternative investment possibilities. We
Finally, we
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, implied volatility and implied Sharpe ratio
and implied volatility