2009-2010 FINANCIAL MATHEMATICS SEMINAR

Unless otherwise noted, the seminars take place on 4:30 pm on Friday, in Room 133 of Eckhart Hall.

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Open to the public.

More speakers will be added over time. The listed speakers are confirmed unless otherwise noted.

Date Speaker Affiliation Title of Talk
(click for abstract)		 Comments
10/30/2009
Downtown 		Conference on Liquidity, Credit Risk, and Extreme Events
11/6/2009 Sergei Levendorskii University of Leicester Prices and sensitivities of barrier options near barrier and convergence of Carr's randomization
11/20/2009
Downtown
Quantitative Finance on Fridays		 George Constantinides University of Chicago The Puzzle of Index Option Returns

ABSTRACTS

Prices and sensitivities of barrier options near barrier and convergence of Carr's randomization
Sergei Levendorskii
University of Leicester
The leading term of asymptotics of prices and sensitivities of barrier options and first touch digitals near the barrier for wide classes of L\'evy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In particular, it is proved that option's delta is unbounded for processes of infinite variation, and for processes of finite variation and infinite intensity, with zero drift and drift pointing from the barrier. Two-term asymptotic formulas are also derived. The convergence of prices, sensitivities and the first two terms of asymptotics in Carr's randomization algorithm is proved. Finally, it is proved that, in each case, and for any $m\in Z_+$, the error of Carr's randomization approximation can be represented  in the form $\sum_{j=1}^m c_j(T,x)N^{-j} +O(N^{-j})$, where $N$ is the number of time steps. This justifies not only Richardson extrapolation but extrapolations of higher order as well.

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