Indifference Prices and Implied Volatility under Local-Stochastic Volatility

Summary

The paper derives approximations for buyer and seller indifference prices for European contingent claims in a general local-stochastic volatility setting. The investor is assumed to have exponential utility, and the claim payoff can depend on either a traded asset or a non-traded asset. Indifference prices represent the levels at which the investor would be willing to buy or sell the claim given the modeled risks and preferences.

For European calls on a traded asset, the authors translate the price approximations into buyer and seller implied volatility surfaces. For claims on non-traded assets, they establish rigorous error bounds for the price approximation. They illustrate the methods with two examples. The supplied description does not give the approximation formulas, numerical findings, or assumptions beyond the model and utility specification, so it offers no basis for judging accuracy across market conditions or for treating the approximations as universal pricing rules.

Key ideas

• The analysis assumes exponential utility within a general local-stochastic volatility model.
• It approximates buyer and seller indifference prices for European claims tied to traded or non-traded assets.
• For calls on traded assets, the price approximations yield corresponding buyer and seller implied volatility surfaces.
• For non-traded asset claims, the paper establishes error bounds for its price approximation.
• Two examples illustrate the methods, but the supplied description does not report their numerical outcomes.

Tags

# Indifference prices and implied volatilities


# Indifference prices and implied volatilities









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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