OPTIMAL STATIC–DYNAMIC HEDGES FOR BARRIER OPTIONS

Aytaç İlhan and Ronnie Sircar

Mathematical Finance, 2006, vol. 16, issue 2, 359-385

Abstract: We study optimal hedging of barrier options, using a combination of a static position in vanilla options and dynamic trading of the underlying asset. The problem reduces to computing the Fenchel–Legendre transform of the utility‐indifference price as a function of the number of vanilla options used to hedge. Using the well‐known duality between exponential utility and relative entropy, we provide a new characterization of the indifference price in terms of the minimal entropy measure, and give conditions guaranteeing differentiability and strict convexity in the hedging quantity, and hence a unique solution to the hedging problem. We discuss computational approaches within the context of Markovian stochastic volatility models.

Date: 2006
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