TY - JOUR
T1 - A simulation approach to financial options Greeks estimation under Lévy processes
AU - Liu, Gang
AU - Cui, Zhenyu
AU - Liu, Yanchu
AU - Xie, Jingui
PY - 2017
Y1 - 2017
N2 - 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 Levy processes. For asset price models following Levy 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.
AB - 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 Levy processes. For asset price models following Levy 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.
KW - Characteristic function
KW - Greeks
KW - Levy process
KW - Pathwise derivative method
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U2 - 10.3969/j.issn.0253-2778.2017.03.009
DO - 10.3969/j.issn.0253-2778.2017.03.009
M3 - Article
AN - SCOPUS:85026274071
SN - 0253-2778
VL - 47
SP - 262
EP - 266
JO - Journal of University of Science and Technology of China
JF - Journal of University of Science and Technology of China
IS - 3
ER -