Exponential hedging with optimal stopping and application to employee stock option valuation

T. I.M. Leung, Ronnie Sircar

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We study the problem of hedging early exercise (American) options with respect to exponential utility within a general incomplete market model. This leads us to construct a duality formula involving relative entropy minimization and optimal stopping. We further consider claims with multiple exercises, and static-dynamic hedges of American claims with other European and American options. The problem is important for accurate valuation of employee stock options (ESOs), and we demonstrate this in a standard diffusion model. We find that incorporating static hedges with market-traded options induces the holder to delay exercises and increases the ESO cost to the firm.

Original languageEnglish (US)
Pages (from-to)1422-1451
Number of pages30
JournalSIAM Journal on Control and Optimization
Volume48
Issue number3
DOIs
StatePublished - Jun 30 2009

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • American options
  • Employee stock options
  • Financial mathematics
  • Optimal stopping
  • Utility indifference pricing

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