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International Journal of Stochastic AnalysisVolume 2011 2011, Article ID 435145, 27 pages

Research Article

Mathematical and Computational Finance Laboratory, Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive NW, Atlanta, GA 30332, USA

Received 16 December 2010; Revised 9 March 2011; Accepted 16 March 2011

Academic Editor: Kambiz Farahmand

Copyright © 2011 Anatoliy Swishchuk and Li Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the valuation of the variance swaps under stochastic volatility with delayand jumps. In our model, the volatility of the underlying stock price process not onlyincorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time depends not only onthe situation at but also on the whole past history of the process up to time as well. The jump part in our model is finally represented by a general version of compoundPoisson processes. We provide some analytical closed forms for the expectation of therealized variance for the stochastic volatility with delay and jumps. We also present alower bound for delay as a measure of risk. As applications of our analytical solutions,a numerical example using SandP60 Canada Index 1998–2002 is then provided to pricevariance swaps.

Author: Anatoliy Swishchuk and Li Xu



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