Calibration and simulation of Heston model

• Autorzy: Milan Mrázek , Jan Pospíšil
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Heston model; Stochastic volatility; Option pricing; Monte Carlo simulation; Calibration

Kategorie tematyczne

• 91G20: Derivative securities
• 91G60: Numerical methods (including Monte Carlo methods)
• 65K10: Optimization and variational techniques
• 60H10: Stochastic ordinary differential equations
• 60H35: Computational methods for stochastic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 679-704

Daty

wydano

2017-01-01

otrzymano

2016-07-29

zaakceptowano

2017-04-10

online

2017-05-23

Twórcy

autor

Milan Mrázek

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autor

Jan Pospíšil

• , , 8, , ,

Identyfikatory

DOI

10.1515/math-2017-0058