Abstract
In this paper, we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the jump part in the underlying model dynamics. Also an impact of the long memory parameter is measured for the approximative fractional SV model (FSV). For the first time, the robustness of calibrated models is measured using bootstrapping methods on market data and Monte Carlo filtering techniques. In contrast to several other sensitivity analysis approaches for SV models, the newly proposed methodology does not require independence of calibrated parameters—an assumption that is typically not satisfied in practice. Empirical study is performed on a data set of Apple Inc. equity options traded in four different days in April and May 2015. In particular, the results for Heston, Bates and approximative FSV models are provided.
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Notes
For more details on the arbitrage pricing see, for instance, Shreve (2004).
Alternatively one can estimate the parameters from time-series data.
The weight functions introduced by Mrázek et al. (2016) were considered.
For instance, if \(N = 6\) one might obtain \(\mathbf{X}^{\dagger } = (X_2, X_1,X_4,X_4,X_3,X_2)\) where \(X_j=(K_j,T_j)\).
For more details on Monte Carlo filtering approaches see, for instance Saltelli et al. (2008).
In this case, we will not be able to decide whether the parameters lead to a good or bad description of the modelled market.
For all trials we use “standard” \(\alpha = 5\%\) level of significance. In most of the trials we could have even lower \(\alpha \) and still we would reject the null hypothesis.
See, e.g., www.mathworks.com/help/stats/kstest2.html.
All results and data are available in supplementary materials.
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Acknowledgements
This work was supported by the GACR Grant 14-11559S Analysis of Fractional Stochastic Volatility Models and their Grid Implementation. Computational resources were provided by the CESNET LM2015042 and the CERIT Scientific Cloud LM2015085, provided under the programme “Projects of Large Research, Development, and Innovations Infrastructures”.
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Pospíšil, J., Sobotka, T. & Ziegler, P. Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure. Empir Econ 57, 1935–1958 (2019). https://doi.org/10.1007/s00181-018-1535-3
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DOI: https://doi.org/10.1007/s00181-018-1535-3
Keywords
- Robustness analysis
- Sensitivity analysis
- Stochastic volatility models
- Bootstrapping
- Monte Carlo filtering