An option pricing model based on jump telegraph processes |
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Authors: | Nikita Ratanov |
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Institution: | Universidad del Rosario, C.14, No.4-69, Bogotá, Colombia |
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Abstract: | 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) |
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