Calibration and simulation of Heston model

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Calibration and simulation of Heston model

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Calibration and simulation of Heston model

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-11559S" target="_blank" >GA14-11559S: Analýza frakcionálních modelů stochastické volatility a jejich implementace v gridu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Open Mathematics

ISSN

2391-5455

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

26

Strana od-do

679-704

Kód UT WoS článku

000404576900001

EID výsledku v databázi Scopus

2-s2.0-85021093010