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GREEKS FORMULAS FOR AN ASSET PRICE MODEL WITH GAMMA PROCESSES
Author(s) -
Kawai Reiichiro,
Takeuchi Atsushi
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00452.x
Subject(s) - greeks , girsanov theorem , malliavin calculus , mathematics , mathematical economics , asset (computer security) , brownian motion , variance (accounting) , econometrics , economics , stochastic differential equation , mathematical analysis , computer science , financial economics , statistics , partial differential equation , stochastic partial differential equation , computer security , accounting
Greeks formulas of Delta, Rho, Vega, and Gamma are derived in closed form for asset price dynamics described by gamma processes and Brownian motions time‐changed by a gamma process. The model considered here includes many well‐known models of practical interest, such as the variance gamma model and the Black–Scholes model. Our approach is based upon the Malliavin calculus for jump processes by making full use of a scaling property of gamma processes with respect to the Girsanov transform. The existence of their variance is investigated. Numerical results are provided to illustrate that the derived Greeks formulas have faster rate of convergence relative to the finite difference method.