Hedging lookback and partial lookback options using Malliavin calculus
(2000) In Applied Mathematical Finance 7(2). p.75100 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 deltahedging, and the wellknown strategy is derived from Itô calculus and the theory of partial differentiable equations. However, hedging pathdependent 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 pathdependent options, and in particular for lookback and partial lookback options.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8f304cb48f81447abde394c0e11c9bbe
 author
 Bermin, HansPeter ^{LU}
 organization
 publishing date
 2000
 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
 external identifiers

 scopus:0010426731
 ISSN
 1350486X
 DOI
 10.1080/13504860010014052
 language
 English
 LU publication?
 yes
 id
 8f304cb48f81447abde394c0e11c9bbe
 date added to LUP
 20170121 16:11:11
 date last changed
 20220130 17:16:33
@article{8f304cb48f81447abde394c0e11c9bbe, 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 deltahedging, and the wellknown strategy is derived from Itô calculus and the theory of partial differentiable equations. However, hedging pathdependent 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 pathdependent options, and in particular for lookback and partial lookback options.}}, author = {{Bermin, HansPeter}}, issn = {{1350486X}}, keywords = {{contingent claims; hedging; lookback options; Malliavin calculus}}, language = {{eng}}, number = {{2}}, pages = {{75100}}, publisher = {{Routledge}}, series = {{Applied Mathematical Finance}}, title = {{Hedging lookback and partial lookback options using Malliavin calculus}}, url = {{http://dx.doi.org/10.1080/13504860010014052}}, doi = {{10.1080/13504860010014052}}, volume = {{7}}, year = {{2000}}, }