Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes

Huang, Jing-Zhi; Wu, Liuren

doi:10.2139/ssrn.411020

Cited by 110 publications

(205 citation statements)

References 59 publications

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“…Black-Scholes (Black and Scholes, 1973), Merton (Merton, 1976), Heston (Heston, 1993), Bates (Bates, 1996), Normal inverse Gaussian (NIG) (see e.g. Barndorff-Nielsen, 1997 and the references therein ), variance Gamma (VG) (Madan and Seneta, 1990), BNS (Barndorff-Nielsen andShepard, 2001, 2002), CGMY (Carr et al, 2002), finite moment log-stable (FMLS) (Carr and Wu, 2003), NIG-CIR model (Carr et al, 2003b), a class of time-changed exponential Lévy models (Carr and Wu, 2004;Huang and Wu, 2004), etc. the characteristic function is available in closed form.…”

Section: Option Valuationmentioning

confidence: 99%

“…Here the process {V t } t 0 is assumed to be independent of the process {X t } t 0 . It is, however, possible to calculate the moment generating function without this assumption (see Huang and Wu, 2004;Carr and Wu, 2004). Lee (2004) treats error bounds for a fast Fourier transform (FFT) implementation of the Fourier transform method and list the generalized Fourier transforms for some common pay-off functions such as e.g.…”

Section: The Nig-cir Modelmentioning

confidence: 99%

See 1 more Smart Citation

Sequential calibration of options

Lindström

Ströjby

Brodén

et al. 2008

Computational Statistics & Data Analysis

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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.

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Section: Option Valuationmentioning

confidence: 99%

Section: The Nig-cir Modelmentioning

confidence: 99%

Sequential calibration of options

Lindström

Ströjby

Brodén

et al. 2008

Computational Statistics & Data Analysis

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show abstract

“…See for example Andersen, Bollerslev, and Diebold (2007), and Busch, Christensen, and Nielsen (2011). 3 Our goal is to assess whether the improvements found in the volatility forecasting 1 See for example Bates (2000Bates ( , 2012, Eraker (2004), Huang and Wu (2004), and Santa-Clara and Yan (2010). 2 See Barndor¤-Nielsen and Shephard (2004Shephard ( , 2006, Huang and Tauchen (2005), and the recent survey in Aït-Sahalia and Jacod (2012).…”

Section: Introductionmentioning

confidence: 99%

Option valuation with observable volatility and jump dynamics

Christoffersen

Feunou

Jeon

2015

Journal of Banking & Finance

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AcknowledgementsWe are grateful to the Bank of Canada, the Global Risk Institute, IFSID, SSHRC and TMX for financial support. Thanks also to Glen Keenleyside for editorial support.iii AbstractUnder very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity dynamics. The volatility and jump intensity dynamics in the model are directly driven by model-free empirical measures of diffusive volatility and jump variation. Because the empirical measures are observed in discrete intervals, our option valuation model is cast in discrete time, allowing for straightforward filtering and estimation of the model. Our model belongs to the affine class, enabling us to derive the conditional characteristic function so that option values can be computed rapidly without simulation. When estimated on S&P500 index options and returns, the new model performs well compared with standard benchmarks.

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“…To filter option price records, we follow the criteria of Carr and Wu (2003, 2009 and Huang and Wu (2004). We delete an option record when the bid price is zero, negative or more than the ask price.…”

Section: Option Pricesmentioning

confidence: 99%

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

Fan¹,

Taylor

Sandri

2017

Journal of Futures Markets

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This paper presents the first comparison of the accuracy of density forecasts for stock prices. Six sets of forecasts are evaluated for DJIA stocks, across four forecast horizons. Two forecasts are risk-neutral densities implied by the Black-Scholes and Heston models. The third set are historical lognormal densities with dispersion determined by forecasts of realized variances obtained from 5-min returns. Three further sets are defined by transforming risk-neutral and historical densities into realworld densities. The most accurate method applies the risk transformation to the Black-Scholes densities. This method outperforms all others for 87% of the comparisons made using the likelihood criterion.

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Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes

Cited by 110 publications

References 59 publications

Sequential calibration of options

Sequential calibration of options

Option valuation with observable volatility and jump dynamics

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

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