From: Brenda Cook (brenda@math.missouri.edu)
Date: Thu Sep 21 2006 - 09:29:24 CDT
SPECIAL SEMINAR ON
MATHEMATICAL FINANCE
University of Missouri-Columbia
Department of Mathematics
Prof. Nikita Ratanov
Universidad del Rosario
A Jump Telegraph Model for Option Pricing
Abstract: A new class of financial market models is proposed. These
models are based on generalized telegraph processes: Markov random flows
with alternating velocities and jumps occurring when the velocities are
switching. While such markets may admit an arbitrage opportunity, the
model under consideration is arbitrage-free and complete if directions
of jumps in stock prices are in a certain correspondence with their
velocity and interest rate behavior. An analog of the Black-Scholes
fundamental differential equation is derived, but, in contrast with the
Black-Scholes model, this equation is hyperbolic. Explicit formulas for
prices of European options are obtained using perfect and quantile hedging.
Friday, September 22, 2006
3:00-4:00 p.m.
312 Math Sciences
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