INDIFFERENCE PRICES AND IMPLIED VOLATILITIES. (26th May 2016)

• Record Type: Journal Article
• Authors: Lorig, Matthew
• Is Part Of: Mathematical finance. Volume 28:Number 1(2018)
• Page Start: 372
• Page End: 408
• Publication Date: 2016-05-26
• Subjects: indifference pricing -- implied volatility -- PDE asymptotics -- local‐stochastic volatility -- Heston; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12129
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: 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 nontraded asset, we derive an explicit approximation for both the buyer's and seller's indifference prices. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surfaces. For European claims on a nontraded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.