[grads] [Sem-coll] AM Dept Colloquium 9/10

[Joe Millham]

Greetings! 
Please join us for the Applied Mathematics Department Colloquium Monday,
Sept. 10 at 4:40 in E1 106.  Coffee and refreshments will be served 10
minutes beforehand.

Speaker: Marek Rutkowski
Topic: Static Replication of Univariate and Bivariate Claims with
Applications to Realized Variance Swaps

Abstract: 
The main goal of this work is to develop a method of static replication of
multi-variate products, such as realized variance swaps, using more standard
products, such as bivariate binary or barrier European calls and puts. In
Section 1, the concept of a static strategy, based on a continuum of traded
call and/or put options, is formally introduced in terms of a measure-valued
portfolio, and relevant quantities are defined and analyzed. We put emphasis
on the fact that the existence of a wealth process of a static strategy is
not always obvious or easy to prove, due to insuficient information about
options prices.
In Section 2, static replication is applied to univariate claims. We first
examine, following Carr and Madan (2002), replication of path-independent
claims with twice differentiable payoffs. Next, we extend this approach to
payoffs given by differences of two convex functions and subsequently to
payoffs given by functions of finite variation. Since in the last case we
consider claims with a possibly discontinuous payoff, we need to postulate
that all binary call and put options are traded (for a similar observation,
see Carr and Chou (2002)).
In Section 3, the static replication of bivariate claims is introduced and
examined. Initially, bivariate functions of finite variation are defined and
it is consequently shown how to replicate claims with payoffs given by
bivariate functions of finite variation. The work concludes by an
application of general results to static hedging of a realized variance
swap.

Thank you and see you there!
Joe Millham
Administrative Assistant
Applied Mathematics Department
312.567.8984
jmillham at iit.edu 


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