Optimal static-dynamic hedges for exotic options under convex risk measures

Aytaç Ilhan, Mattias Jonsson, Ronnie Sircar

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an optimal static position for general convex risk measures, and then analyze in detail the case of shortfall risk with a power loss function. Here we find conditions for uniqueness of the static hedge. We illustrate the computational challenge of computing the market-adjusted risk measure in a simple diffusion model for an option on a non-traded asset.

Original languageEnglish (US)
Pages (from-to)3608-3632
Number of pages25
JournalStochastic Processes and their Applications
Volume119
Issue number10
DOIs
StatePublished - Oct 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Exotic options
  • Hedging
  • Risk measures

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