Calibration and simulation of Heston model. (English) Zbl 1368.60061

Mrázek, Milan; Pospíšil, Jan

Open Math. 15, 679-704 (2017).

Summary: 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.

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
65K10	Numerical optimization and variational techniques
91G20	Derivative securities (option pricing, hedging, etc.)
91G60	Numerical methods (including Monte Carlo methods)

Keywords:

Heston model; stochastic volatility; option pricing; Monte Carlo simulation; calibration

Software:

Mathematica

References:

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