Semi-static hedging of barrier options under poisson jumps

Peter Carr

Research output: Contribution to journalArticle

Abstract

We show that the payoff to barrier options can be replicated when the underlying price process is driven by the difference of two independent Poisson processes. The replicating strategy employs simple semi-static positions in co-terminal standard options. We note that classical dynamic replication using just the underlying asset and a riskless asset is not possible in this context. When the underlying of the barrier option has no carrying cost, we show that the same semi-static trading strategy continues to replicate even when the two jump arrival rates are generalized into positive even functions of distance to the barrier and when the clock speed is randomized into a positive continuous independent process. Since the even function and the positive process need no further specification, our replicating strategies are also semi-robust. Finally, we show that previous results obtained for continuous processes arise as limits of our analysis.

Original languageEnglish (US)
Pages (from-to)1091-1111
Number of pages21
JournalInternational Journal of Theoretical and Applied Finance
Volume14
Issue number7
DOIs
StatePublished - Nov 2011

Fingerprint

Static hedging
Jump
Barrier options
Assets
Poisson process
Costs
Replication
Trading strategies

Keywords

  • arbitrage
  • barrier options
  • hedging jump processes
  • Poisson processes
  • robust valuation
  • Static replication

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)
  • Finance

Cite this

Semi-static hedging of barrier options under poisson jumps. / Carr, Peter.

In: International Journal of Theoretical and Applied Finance, Vol. 14, No. 7, 11.2011, p. 1091-1111.

Research output: Contribution to journalArticle

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