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Greeks Formulas for an Asset Price Model with Gamma Processes

By Reiichiro Kawai and Atsushi Takeuchi

Abstract

Full text of this item is not currently available on the LRA. The final published version may be available through the links above.Greeks formulas of Delta, Rho, Vega, and Gamma are derived in closed formfor asset\ud price dynamics described by gamma processes and Brownian motions time-changed\ud by a gamma process. The model considered here includes many well-known models of\ud practical interest, such as the variance gamma model and the Black–Scholes model.\ud Our approach is based upon the Malliavin calculus for jump processes by making full\ud use of a scaling property of gamma processes with respect to the Girsanov transform.\ud The existence of their variance is investigated. Numerical results are provided to illustrate\ud that the derived Greeks formulas have faster rate of convergence relative to the\ud finite difference method

Topics: Bismut–Elworthy–Li type formulas, gamma processes, Girsanov transform, Malliavin calculus, time-changed Brownian motion, variance gamma processes
Publisher: John Wiley & Sons
Year: 2010
DOI identifier: 10.1111/j.1467-9965.2010.00452.x
OAI identifier: oai:lra.le.ac.uk:2381/9639
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