posted on 2012-03-02, 12:48authored byReiichiro Kawai, Atsuchi Takeuchi
The purpose of this paper is to derive the Greeks formulas of Delta, Gamma, Vega and Theta, for derivative securities
with both continuous and discontinuous payoff structures under asset price dynamics described by stable and tempered
stable processes with presentation of their practical simulation methods. Our approach is based on the representation of
stable distributions using exponential distribution whose scaling property with respect to the Girsanov transform is used
in the Malliavin calculus framework on the Poisson space. Numerical results are presented to illustrate the effectiveness
of our formulas in Monte Carlo simulations relative to the finite difference method.
History
Citation
Quantitative Finance (in press)
Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
This is an electronic version of an article published in Quantitative Finance (in press). Quantitative Finance is available online at: http://www.tandfonline.com/doi/abs/10.1080/14697688.2011.589403