On extracting information implied in options

Benko, Michal; Fengler, Matthias R.; Härdle, Wolfgang Karl; Kopa, Miloš

doi:10.1007/s00180-007-0061-0

Cited by 37 publications

(45 citation statements)

References 12 publications

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“…Finally we compute also the Calendar arbitrage measure as the volume of negative first derivative of total variance, see [2]. In this case we do not observe any violation of Calendar arbitrage free condition.…”

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 92%

“…We use as dataset all the options on DAX listed on 30 December 2011 with all the maturities. Following [2] we compute the unconstrained estimation of the IV surface. In Figure 1 we show the estimation with Epanechnikov kernel function, for moneyness bandwidth 0.04 h κ = and for maturity (calendar) bandwidth 1 h τ = .…”

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

“…Besides each surface we propose also cuts for maturities equal to 168 days and 266 days. The negative parts of SPD violates the moneyness arbitrage free condition, see [2] for more details. Hence, the results show some arbitrage behavior for moneyness around 0.8.…”

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

“…Moreover, to investigate the Arbitrage measure for various types of the kernel functions, we compare the Arbitrage measure for the different kernel functions and for three bandwidths used previously in Table 1. We compute again the IV and SPD surface using unconstraint semiparametric estimation proposed in [2], but now with a non fixed calendar bandwidth. In Figure 5 If we compare these results with those we obtained for fixed calendar bandwidth we can notice that the arbitrage measure seems to smaller for all choices of moneyness bandwidth.…”

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

“…In this paper, and in line with [2], we apply relatively classic approach of local polynomial smoothing techniques and study the bandwidth selection process in more details of recent data of DAX option prices (December 2011). In particular, we change h and examine the impact on the interval of moneyness that brings arbitrage opportunity and on the total degree of noarbitrage violation.…”

Section: Introductionmentioning

confidence: 99%

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On the Implied Volatility Extraction and the Selection of Suitable Kernel

Kopa¹,

Vitali²,

Tichý³

2015

Proceedings of the 2015 International Conference on Computer Science and Intelligent Communication

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Abstract-At the market, we can identify various kinds of options. Some of them are traded at organized exchanges and are quite liquid. Others are traded only between particular parties. The current market practice is to obtain implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. It therefore follows that the BS model at one time moment can be related to the whole set of IVs as given by maturity/moneyness relation of tradable options. One can therefore get IV curve or surface (a so called smirk or smile). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary. However, it can lead to arbitrage opportunity, if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim on the analyses of the behavior of IV and SPD with respect to different choices of bandwidth parameter h and identification of a set of bandwidths which violates no-arbitrage conditions. We document that the change of h implies interesting changes in the violation interval of moneyness. Finally, we also show the impact of h on the total area of SPD under zero, which can be seen as a degree of no-arbitrage violation.

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Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 92%

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

Section: Analysis Concerning the Three Dimensions Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Implied Volatility Extraction and the Selection of Suitable Kernel

Kopa¹,

Vitali²,

Tichý³

2015

Proceedings of the 2015 International Conference on Computer Science and Intelligent Communication

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Implied Volatility Surface Estimation via Quantile Regularization

Maciak¹,

Pešta²,

Vitali³

2020

Analytical Methods in Statistics

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The implied volatility function and the implied volatility surface are both key tools for analyzing financial and derivative markets and various approaches were proposed to estimate theses quantities. On the other hand, theoretical, practical, and also computational pitfalls occur in most of them. An innovative estimation method based on an idea of a sparse estimation and an atomic pursuit approach is introduced to overcome some of these limits: the quantile LASSO estimation implies robustness with respect to common market anomalies; the panel data structure allows for a time dependent modeling; changepoints introduce some additional flexibility in order to capture some sudden changes in the market and linear constraints ensure the arbitrage-free validity; last but not least, the interpolated implied volatility concept overcomes the problem of consecutive maturities when observing the implied volatility over time. Some theoretical backgrounds for the quantile LASSO estimation method are presented, the idea of the interpolated volatilities is introduced, and the proposed estimation approach is applied to estimate the implied volatility of the Erste Group Bank AG call options quoted in EUREX Deutschland Market.

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Option Data and Modeling BSM Implied Volatility

Fengler

2011

Handbook of Computational Finance

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This contribution to the Handbook of Computational Finance, Springer-Verlag, gives an overview on modeling implied volatility data. After introducing the concept of Black-Scholes-Merton implied volatility (IV), the empirical stylized facts of IV data are reviewed. We then discuss recent results on IV surface dynamics and the computational aspects of IV. The main focus is on various parametric, semi-and nonparametric modeling strategies for IV data, including ones which respect no-arbitrage bounds.

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On extracting information implied in options

Abstract: Implied volatility, Nonparametric regression,

Cited by 37 publications

References 12 publications

On the Implied Volatility Extraction and the Selection of Suitable Kernel

On the Implied Volatility Extraction and the Selection of Suitable Kernel

Implied Volatility Surface Estimation via Quantile Regularization

Option Data and Modeling BSM Implied Volatility

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