Optimal static-dynamic hedges for barrier options

Aytaç Ilhan, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)359-385
Number of pages27
JournalMathematical Finance
Volume16
Issue number2
DOIs
StatePublished - Apr 1 2006

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

Keywords

  • Derivative securities
  • Hedging
  • Indifference pricing
  • Stochastic control
  • Stochastic volatility

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