School Seminars and Colloquia

Workshop on Methods for Pricing Financial Options


Half-day International Workshop

by Centre for Actuarial Studies and MASCOS


Institution:
Date: Thu 8th March 2007
Time: 1:00 PM
Location: Theatre 1, Alan Gilbert Building

Abstract: The workshop program consists of four 40 minute-long talks by researchers from three countries.

IMPORTANT: RSVP by Friday, 2 March to Aihua Xia xia@digican.ms.unimelb.edu.au
There is no registration fee for workshop participants, but RSVPs are essential.


WORKSHOP PROGRAM


(1) 1:00-1:50 pm
Mark S. Joshi (Centre for Actuarial Studies, the University of Melbourne)

"Achieving smooth asymptotics for the prices of European options in binomial trees"
Abstract: A new binomial approximation to the Black-Scholes model is
introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of 1/n exists. This is the first binomial tree for which such an
asymptotic expansion has been shown to exist.


(2) 1:50-2:40 pm
Andrew Lyasoff (Boston University)

"Asian Options and Perpetuities Revisited"
Abstract: A new approach to the study of the distribution law of the integral of geometric Brownian motion will be presented. In particular, we will show that the well known integral representation for the density due to M. Yor is just one extreme case in a cluster of formulas in which the density can be expressed as a double integral. We will show that one of these representations leads to a closed formula for the price of Asian options in the form of double integral. Some new numerical approximation
procedures for the density of the integral of geometric Brownian motion will be discussed.


*2:40-3:10 Coffee Break


3:10-4:00 pm
Daniel Dufresne (Centre for Actuarial Studies, the University of Melbourne)

"New Results on the Integral of Geometric Brownian motion"
Abstract: Some new results on the integral of geometric Brownian motion are presented, in particular: series expressions for the density,
logarithmic moments, identities in distribution. Joint work with Marc Yor
(in part).


(4) 4:00-4:50 pm
Dr. Anastasia Kolodko (Weierstrass Institute for Applied Analysis and
Stochastics, Berlin)

"Iterative procedure for pricing Bermudan options"
Abstract: We present an iterative procedure for computing the optimal
Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many
steps. Then, by duality, the method induces a convergent sequence of upper bounds as well. In a Markovian setting the presented method allows to
calculate approximative solutions with only one nesting of conditional
expectations and is therefore tailor-made for a plain Monte-Carlo implementation. The power of the procedure is demonstrated by pricing
cancelable snowball swap in a full factor LIBOR market model.


*5:00 pm - Post-workshop Drinks & Nibbles at MASCOS (139 Barry Street, Carlton)

For More Information: Aihua Xia: xia@digican.ms.unimelb.edu.au