Title: A non-Markov model for volatility jumps

Authors: V. Arunachalam; L. Blanco; S. Dharmaraja

Addresses: Department of Mathematics, University of Los Andes, AA 4976, Bogotá, Colombia. ' Department of Statistics, National University of Colombia, Carrera 30, No. 45-03, Bogotá, Colombia. ' Department of Mathematics, Indian Institute of Technology, Delhi Hauz Khas, New Delhi 110016, India

Abstract: Volatility has a significant role to play in the determination of risk and in the valuation of options and other financial derivatives. The well-known Black-Scholes model for the financial derivatives deals with constant volatility. This paper presents a new model based on shot noise behaviour, in which the volatility jump occurs in random instant of times. The closed form solution is derived for the proposed model. Further, numerical results are illustrated to validate the above observations.

Keywords: option pricing; volatility jumps; shot noise; non-Markov models; financial derivatives.

DOI: 10.1504/IJFMD.2011.042602

International Journal of Financial Markets and Derivatives, 2011 Vol.2 No.3, pp.223 - 235

Published online: 18 Sep 2011 *

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