Hedging lookback and partial lookback options using Malliavin calculus

Hans-Peter Bermin

Research output: Contribution to journalArticlepeer-review

9 Citations (SciVal)

Abstract

The paper considers a Black and Scholes economy with constant coefficients. A contingent claim is said to be simple if the payoff at maturity is a function of the value of the underlying security at maturity. To replicate a simple contingent claim one uses so called delta-hedging, and the well-known strategy is derived from Itô calculus and the theory of partial differentiable equations. However, hedging path-dependent options require other tools since the price processes, in general, no longer have smooth stochastic differentials. It is shown how Malliavin calculus can be used to derive the hedging strategy for any kind of path-dependent options, and in particular for lookback and partial lookback options.
Original languageEnglish
Pages (from-to)75-100
Number of pages26
JournalApplied Mathematical Finance
Volume7
Issue number2
DOIs
Publication statusPublished - 2000

Subject classification (UKÄ)

  • Economics

Keywords

  • contingent claims
  • hedging
  • lookback options
  • Malliavin calculus

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