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An option pricing model based on jump telegraph processes
Author(s) -
Ratanov Nikita
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700351
Subject(s) - arbitrage , jump , black–scholes model , valuation of options , quantile , economics , stochastic differential equation , mathematical economics , mathematics , jump diffusion , financial market , econometrics , financial economics , physics , volatility (finance) , finance , quantum mechanics
A new class of financial market models is developed. 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 behaviour. 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)