Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Pospı́šil, J.; Sobotka, Tomáš; Ziegler, Philipp

doi:10.1007/s00181-018-1535-3

Cited by 9 publications

(18 citation statements)

References 27 publications

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“…A special attention is nowadays paid to models with fractional volatility, we refer to recent paper by Pospíšil and Sobotka [49] where a new approximative fractional stochastic volatility jump diffusion model is presented and compared to the Heston model. In [50], authors also study the robustness and sensitivity analysis of these two models.…”

Section: Resultsmentioning

confidence: 99%

Calibration and simulation of Heston model

Mrázek

Pospı́šil

2017

Open Mathematics

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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.

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Section: Resultsmentioning

confidence: 99%

Calibration and simulation of Heston model

Mrázek

Pospı́šil

2017

Open Mathematics

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“…It not only shows the superiority of the proposed design method but corresponds to that the PD feedback scheme can be reasonably used in the case of the high accuracy state observer. The sensitivity and robustness analysis methods usually provide useful information to the development of control systems [37,38]. To enhance the robustness to disturbances The sensitivity and robustness analysis methods usually provide useful information to the development of control systems [37,38].…”

Section: ( ) [ ]mentioning

confidence: 99%

“…The sensitivity and robustness analysis methods usually provide useful information to the development of control systems [37,38]. To enhance the robustness to disturbances The sensitivity and robustness analysis methods usually provide useful information to the development of control systems [37,38]. To enhance the robustness to disturbances and the sensitivity to faults, it is necessary to measure the robustness and sensitivity by a suitable performance index and optimize it.…”

Section: ( ) [ ]mentioning

confidence: 99%

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

2021

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This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

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“…The sensitivity and robustness analysis methods usually provide useful information to the development of control systems [34, 35]. In order to enhance the robustness to disturbances and the sensitivity to faults, it is necessary to measure the robustness and sensitivity by a suitable performance index and optimize it.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The robustness and sensitivity analysis of control systems with respect to the parametric variations of the controlled plant is not the major goal of this paper. However, it is worth mentioning that the robustness and sensitivity analysis methods [34, 35] could help designers to extend the proposed control approach to investigate the robust fuzzy control for the perturbed nonlinear singular systems.…”

Section: Numerical Examplesmentioning

confidence: 99%

Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

Chang

Varadarajan

2020

Asian Journal of Control

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This paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi‐Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi‐Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

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Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Cited by 9 publications

References 27 publications

Calibration and simulation of Heston model

Calibration and simulation of Heston model

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

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