Hedging lookback and partial lookback options using Malliavin calculus
(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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http://lup.lub.lu.se/record/8f304cb4-8f81-447a-bde3-94c0e11c9bbe
- author
- Bermin, Hans-Peter ^{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
- 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
- 2018-05-29 11:23:51
@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}, }