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Sequential calibration of options

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  • Lindström, Erik
  • Ströjby, Jonas
  • Brodén, Mats
  • Wiktorsson, Magnus
  • Holst, Jan

Abstract

Robust calibration of option valuation models to quoted option prices is non-trivial but crucial for good performance. A framework based on the state-space formulation of the option valuation model is introduced. Non-linear (Kalman) filters are needed to do inference since the models have latent variables (e.g. volatility). The statistical framework is made adaptive by introducing stochastic dynamics for the parameters. This allows the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently. The performance and computational efficiency of standard and iterated extended Kalman filters (EKF and IEKF) are investigated. These methods are compared to common calibration such as weighted least squares (WLS) and penalized weighted least squares (PWLS). A simulation study, using the Bates model, shows that the adaptive framework is capable of tracking time varying parameters and latent processes such as stochastic volatility processes. It is found that the filter estimates are the most accurate, followed by the PWLS estimates. The estimates from all of the advanced methods are significantly closer to the true parameters than the WLS estimates which overfits data. The filters are also faster than least squares methods. All calibration methods are also applied to daily European option data on the S&P 500 index, where the Heston, Bates and NIG-CIR models are considered. The results are similar to the simulation study and it can be seen that the overfitting is a real problem for the WLS estimator when applied complex models.

Suggested Citation

  • Lindström, Erik & Ströjby, Jonas & Brodén, Mats & Wiktorsson, Magnus & Holst, Jan, 2008. "Sequential calibration of options," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2877-2891, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2877-2891
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    Cited by:

    1. Foschi, Paolo & Pascucci, Andrea, 2009. "Calibration of a path-dependent volatility model: Empirical tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2219-2235, April.
    2. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    3. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    4. Pascal François & Lars Stentoft, 2021. "Smile‐implied hedging with volatility risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1220-1240, August.
    5. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    6. Fig-Talamanca, Gianna, 2009. "Testing volatility autocorrelation in the constant elasticity of variance stochastic volatility model," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2201-2218, April.
    7. Josef Danv{e}k & J. Posp'iv{s}il, 2020. "Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models," Papers 2006.13181, arXiv.org.
    8. Emese Lazar & Shuyuan Qi & Radu Tunaru, 2020. "Measures of Model Risk in Continuous-time Finance Models," Papers 2010.08113, arXiv.org, revised Oct 2020.
    9. Lindström, Erik, 2013. "Tuned iterated filtering," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2077-2080.

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