Hedging under gamma constraints by optimal stopping and face-lifting

H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

A super-replication problem with a gamma constraint, introduced in Soner and Touzi, is studied in the context of the one-dimensional Black and Scholes model. Several representations of the minimal super-hedging cost are obtained using the characterization derived in Cheridito, Soner, and Touzi. It is shown that the upper bound constraint on the gamma implies that the optimal strategy consists in hedging a conveniently face-lifted payoff function. Further an unusual connection between an optimal stopping problem and the lower bound is proved. A formal description of the optimal hedging strategy as a succession of periods of classical Black-Scholes hedging strategy and simple buy-and-hold strategy is also provided.

Original languageEnglish (US)
Pages (from-to)59-79
Number of pages21
JournalMathematical Finance
Volume17
Issue number1
DOIs
StatePublished - Jan 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • Hedging under constraints
  • Optimal stopping
  • Stochastic control

Fingerprint Dive into the research topics of 'Hedging under gamma constraints by optimal stopping and face-lifting'. Together they form a unique fingerprint.

  • Cite this