Colloquium
3:00 p.m., Friday (November 12, 2004)
Math Annex 1100
Sebastian Ferrando
Ryerson University
Martingales and Wavelets: Applications to Hedging Financial Derivatives
We will describe a new discretization of financial instruments
in terms of a martingale expansion constructed using Haar wavelets systems.
In particular, expansions on these bases give the pointwise convergence
needed for hedging derivatives. Examples of these systems are constructed
which illustrate the discrete, spacewise, nature of the approximations.
We describe natural conditions under which our Haar hedging strategy can
be realized by means of a self financing portfolio consisting of binary
options. We will explain how basic ideas from wavelet theory allows us to
construct efficient approximations to a given financial portfolio X . This
allows to reduce transaction costs in the financial implementation of Haar
hedging.
Little background will be assumed, in particular, the basic ideas behind
hedging financial derivatives and the role of martingales will be explained.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
