Calibration and simulation of Heston model

Milan Mrázek, and Jan Pospíšil. "Calibration and simulation of Heston model." Open Mathematics 15.1 (2017): 679-704. <http://eudml.org/doc/288332>.

@article{MilanMrázek2017,
abstract = {We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods. We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.},
author = {Milan Mrázek, Jan Pospíšil},
journal = {Open Mathematics},
keywords = {Heston model; Stochastic volatility; Option pricing; Monte Carlo simulation; Calibration},
language = {eng},
number = {1},
pages = {679-704},
title = {Calibration and simulation of Heston model},
url = {http://eudml.org/doc/288332},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Milan Mrázek
AU - Jan Pospíšil
TI - Calibration and simulation of Heston model
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 679
EP - 704
AB - We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods. We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.
LA - eng
KW - Heston model; Stochastic volatility; Option pricing; Monte Carlo simulation; Calibration
UR - http://eudml.org/doc/288332
ER -