Static hedging under time-homogeneous diffusions

Peter Carr, Sergey Nadtochiy

Research output: Contribution to journalArticle

Abstract

We consider the problem of semistatic hedging of a single barrier option in a model where the underlying is a time-homogeneous diffusion, possibly running on an independent stochastic clock. The main result of the paper is an analytic expression for the payoff of a European-type contingent claim, which has the same price as the barrier option up to hitting the barrier. We then consider some examples, such as the Black-Scholes, constant elasticity of variance, and zero-correlation SABR models. Finally, we investigate an approximation of the static hedge with options of at most two different strikes.

Original languageEnglish (US)
Pages (from-to)794-838
Number of pages45
JournalSIAM Journal on Financial Mathematics
Volume2
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Barrier options
  • Inverse transform
  • Method of images
  • Static hedging
  • Sturm-liouville theory
  • Time-homogeneous diffusions

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics

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