A simulation approach to financial options Greeks estimation under Lévy processes

Accurate estimation of the Greeks for financial options is an important practical procedure for risk management of financial derivatives. It is also an important topic in financial engineering research. Monte Carlo simulation method, being capable of avoiding the problem of “curse of dimensionality”, is one of the most popular computational tools in financial engineering. Here a new Monte Carlo simulation method was developed to estimate Greeks for financial options under Lévy processes. For asset price models following Lévy processes, only the characteristic functions are known. By building our method on Fourier transform inversion and linear interpolations, approximations of the cumulative distribution functions and the probability density functions can be obtained, paving the way for generating random samples and constructing Monte Carlo simulation estimates to the Greeks. Numerical experiments were conducted to illustrate the efficiency of the proposed method and the results show that it performs more efficiently than alternatives in the literature.