Calibration and simulation of Heston model
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43930092" target="_blank" >RIV/49777513:23520/17:43930092 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/math-2017-0058" target="_blank" >http://dx.doi.org/10.1515/math-2017-0058</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/math-2017-0058" target="_blank" >10.1515/math-2017-0058</a>
Alternative languages
Result language
angličtina
Original language name
Calibration and simulation of Heston model
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA14-11559S" target="_blank" >GA14-11559S: Analysis of Fractional Stochastic Volatility Models and their Grid Implementation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Open Mathematics
ISSN
2391-5455
e-ISSN
—
Volume of the periodical
15
Issue of the periodical within the volume
1
Country of publishing house
PL - POLAND
Number of pages
26
Pages from-to
679-704
UT code for WoS article
000404576900001
EID of the result in the Scopus database
2-s2.0-85021093010