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Hedging lookback and partial lookback options using Malliavin calculus

Bermin, Hans-Peter LU (2000) In Applied Mathematical Finance 7(2). p.75-100
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
contingent claims, hedging, lookback options, Malliavin calculus
in
Applied Mathematical Finance
volume
7
issue
2
pages
26 pages
publisher
Routledge
ISSN
1350-486X
DOI
10.1080/13504860010014052
language
English
LU publication?
yes
id
8f304cb4-8f81-447a-bde3-94c0e11c9bbe
date added to LUP
2017-01-21 16:11:11
date last changed
2017-02-14 08:28:44
@article{8f304cb4-8f81-447a-bde3-94c0e11c9bbe,
  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.},
  author       = {Bermin, Hans-Peter},
  issn         = {1350-486X},
  keyword      = {contingent claims,hedging,lookback options,Malliavin calculus},
  language     = {eng},
  number       = {2},
  pages        = {75--100},
  publisher    = {Routledge},
  series       = {Applied Mathematical Finance},
  title        = {Hedging lookback and partial lookback options using Malliavin calculus},
  url          = {http://dx.doi.org/10.1080/13504860010014052},
  volume       = {7},
  year         = {2000},
}