Sydney Financial Mathematics Workshop
Sponsored by
National Australia Bank
Workshops on the Malliavin Calculus
Alan Brace (NAB) and Ben Goldys (UNSW)
| Time: | 5:15--7:00 pm |
| Date: | Wednesday, 19 July;
Wednesday, 2 August;
Monday, 14 August;
Wednesday, 30 August 2000. |
| Venue: | Ground Floor, AAP Seminar Room, 259 George St |
Abstract
The first 4 workshops will cover the basics of Malliavin Calculus, including:
Wiener chaos, the Malliavin derivative, the Skorohod integral, and the
derivative of a process. The approach adopted is to follow Sections 1.1, 1.2,
1.3, 2.2 and 2.3.1 of David Nualart's excellent book:
Additional notes are being prepared by the presenters and will be distributed
to interested delegates. Ben & Alan aim to do things slowly and properly,
concentrating on lots of simple examples to decode ideas and illustrate
structures.
What is Malliavin calculus ?
Malliavin calculus involves two adjoint operators: the first is the Malliavin
derivative, and the second is the Skorohod integral which collapses to the Ito
integral for adapted processes. That produces an integration-by-parts formula
with the Ito integral on one side and the Malliavin derivative on the other,
thus considerably extending the (essential to financial mathematicians) tool
of stochastic integration.
What use does Malliavin Calculus have in Finance ?
Among other things, Malliavin calculus is useful for calculating Greeks where
the expectation of the messy derivative of the payoff with respect to some
initial condition can be converted into an expectation of the clean payoff,
times an adjustment factor. These results come into their own when simulating
Greeks as is shown in the paper by Fournie et al mentioned above.
What level of expertise do I need ?
People who attend should be au fait with stochastic calculus and be prepared
to do some serious work. The presenters however, hope and expect to reduce
the pain of learning to a relative minimum.
References
-
Nualart, D. "The Malliavin calculus and related topics"
Springer-Verlag 1995 (ISBN 0-387-94432-X)
-
Fournie E, Lasry JM, Lebuchoux J, Lions PL, Touzi N (1999)
"Applications of Malliavin calculus to Monte Carlo methods
in finance", Finance and Stochastics, 3, 391-412.
Please feel free to bring this to the attention of interested colleagues.