Computation of Greeks for asset price dynamics driven by stable and tempered stable processes

Abstract

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 an 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.

Keywords:

• CGMY process
• Finite difference method
• Greeks
• Lévy process
• Malliavin calculus
• Monte Carlo simulation
• Sensitivity analysis