ROBUST TRADING OF IMPLIED SKEW

In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific model — i.e. the method is robust. The strategy is given explicitly and depends only on one’s beliefs about the future values of implied skewness, which is an observable market indicator. As such, our method allows the use of existing statistical tools to formulate the beliefs, providing a practical interpretation of the more abstract mathematical setting, in which the beliefs are understood as a family of probability measures. One of the applications of the results established herein is a method for trading one’s views on the future changes in implied skew, largely independently of other market factors. Another application of our results provides a concrete improvement of the model-independent super-replication and sub-replication strategies for barrier options proposed in [H. Brown, D. Hobson & L. C. G. Rogers (2001) Robust hedging of barrier options, Mathematical Finance 11 (3), 285–314.], which exploits the given beliefs on the implied skew. Our theoretical results are tested empirically, using the historical prices of S&P 500 options.

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Becoming Politicized

Zeitschrift für Psychologie ◽

10.1027/2151-2604/a000311 ◽

2017 ◽

Vol 225 (4) ◽

pp. 324-335 ◽

Cited By ~ 2

Author(s):

Dimitrios Barkas ◽

Xenia Chryssochoou

Keyword(s):

Collective Identity ◽

Political Socialization ◽

Greek Society ◽

Economic Vulnerability ◽

The World ◽

The Future ◽

Identity Model ◽

Beliefs About The Future ◽

Of Greece ◽

The Way

Abstract. This research took place just after the end of the protests following the killing of a 16-year-old boy by a policeman in Greece in December 2008. Participants (N = 224) were 16-year-olds in different schools in Attiki. Informed by the Politicized Collective Identity Model ( Simon & Klandermans, 2001 ), a questionnaire measuring grievances, adversarial attributions, emotions, vulnerability, identifications with students and activists, and questions about justice and Greek society in the future, as well as about youngsters’ participation in different actions, was completed. Four profiles of the participants emerged from a cluster analysis using representations of the conflict, emotions, and identifications with activists and students. These profiles differed on beliefs about the future of Greece, participants’ economic vulnerability, and forms of participation. Importantly, the clusters corresponded to students from schools of different socioeconomic areas. The results indicate that the way young people interpret the events and the context, their levels of identification, and the way they represent society are important factors of their political socialization that impacts on their forms of participation. Political socialization seems to be related to youngsters’ position in society which probably constitutes an important anchoring point of their interpretation of the world.

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Collective futures: How our beliefs about the future of society are related to our actions and attitudes today

PsycEXTRA Dataset ◽

10.1037/e627722013-008 ◽

2013 ◽

Author(s):

Paul Bain

Keyword(s):

The Future ◽

Beliefs About The Future

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Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

Foundations of Computational Mathematics ◽

10.1007/s10208-021-09536-6 ◽

2021 ◽

Author(s):

Radu Boţ ◽

Guozhi Dong ◽

Peter Elbau ◽

Otmar Scherzer

Keyword(s):

Linear Operator ◽

Operator Equation ◽

Convex Analysis ◽

Convergence Rates ◽

Linear Operator Equation ◽

Optimal Convergence Rates ◽

Ill Posed ◽

Thresholding Algorithm ◽

The Given ◽

Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

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An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽

10.3390/math9090994 ◽

2021 ◽

Vol 9 (9) ◽

pp. 994

Author(s):

Elisa Alòs ◽

Jorge A. León

Keyword(s):

Malliavin Calculus ◽

Numerical Experiments ◽

Implied Volatility ◽

Natural Approach ◽

Volatility Models ◽

Implied Volatility Surface ◽

Short Memory ◽

White Type ◽

Volatility Surface ◽

Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

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Sinai and Exodus: Two Grounds for Hope in the Jewish Tradition

Religious Studies ◽

10.1017/s0034412500010878 ◽

1978 ◽

Vol 14 (3) ◽

pp. 373-387

Author(s):

David Hartman

Keyword(s):

Jewish Tradition ◽

Look Ahead ◽

The World ◽

The Future ◽

Sole Criterion ◽

The Given ◽

Better Than

Hope is a category of transcedence, by means of which a man does not permit what he senses and experiences to be the sole criterion of what is possible. It is the belief or the conviction that present reality (what I see) does not exhaust the potentialities of the given data. Hope opens the present to the future; it enables a man to look ahead, to break the fixity of what he observes, and to perceive the world as open-textured. The categories of possibility and of transcendence interweave a closely stitched fabric - hope says that tomorrow can be better than today.

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Optimising the AR Engraved Structure on Light-Guide Facets for a Wide Range of Wavelengths

Optics ◽

10.3390/opt2010002 ◽

2020 ◽

Vol 2 (1) ◽

pp. 25-42

Author(s):

Ioseph Gurwich ◽

Yakov Greenberg ◽

Kobi Harush ◽

Yarden Tzabari

Keyword(s):

Theoretical Analysis ◽

Light Guide ◽

Spectral Band ◽

Angular Range ◽

The Past ◽

Input And Output ◽

Wide Range ◽

The Given ◽

Theoretical Results ◽

Shape And Size

The present study is aimed at designing anti-reflective (AR) engraving on the input–output surfaces of a rectangular light-guide. We estimate AR efficiency, by the transmittance level in the angular range, determined by the light-guide. Using nano-engraving, we achieve a uniform high transmission over a wide range of wavelengths. In the past, we used smoothed conical pins or indentations on the faces of light-guide crystal as the engraved structure. Here, we widen the class of pins under consideration, following the physical model developed in the previous paper. We analyze the smoothed pyramidal pins with different base shapes. The possible effect of randomization of the pins parameters is also examined. The results obtained demonstrate optimized engraved structure with parameters depending on the required spectral range and facet format. The predicted level of transmittance is close to 99%, and its flatness (estimated by the standard deviation) in the required wavelengths range is 0.2%. The theoretical analysis and numerical calculations indicate that the obtained results demonstrate the best transmission (reflection) we can expect for a facet with the given shape and size for the required spectral band. The approach is equally useful for any other form and of the facet. We also discuss a simple way of comparing experimental and theoretical results for a light-guide with the designed input and output features. In this study, as well as in our previous work, we restrict ourselves to rectangular facets. We also consider the limitations on maximal transmission produced by the size and shape of the light-guide facets. The theoretical analysis is performed for an infinite structure and serves as an upper bound on the transmittance for smaller-size apertures.

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Sensitivity on the electromagnetic dipole moments of the tau-lepton at the CLIC

10.21468/scipostphysproc.1.045 ◽

2019 ◽

Author(s):

MARIA HERNANDEZ ◽

Ahmet A. Billur ◽

Murat Köksal ◽

Alejandro Gutiérrez-Rodríguez

Keyword(s):

Electric Dipole ◽

Linear Collider ◽

Dipole Moments ◽

Tau Lepton ◽

Good Prospect ◽

Electric Dipole Moments ◽

Systematic Uncertainties ◽

The Future ◽

Model Independent

In this paper we established model independent bounds on the anomalous magnetic and electric dipole moments of the tau-lepton using the process \mathbf{\gamma\gamma \to \tau^+\tau^-}𝛄𝛄→𝛕+𝛕−. We use data collected with the future \mathbf{e^+ e^-}𝐞+𝐞− linear collider such as the CLIC at \mathbf{\sqrt{s}}𝐬 = 380, 1500, 3000 GeV, and we consider systematic uncertainties of \mathbf{\delta_{sys}}𝛅𝐬𝐲𝐬 = 0\%%, 3\%%, 5\%%. The theory predictions are a very good prospect for probing the dipole moments of the tau-lepton at the future \mathbf{e^ + e^-}𝐞+𝐞− linear collider at the \mathbf{\gamma\gamma}𝛄𝛄 mode.

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Threshold Treewidth and Hypertree Width

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/263 ◽

2020 ◽

Author(s):

Robert Ganian ◽

Andre Schidler ◽

Manuel Sorge ◽

Stefan Szeider

Keyword(s):

Constraint Satisfaction ◽

Constraint Satisfaction Problem ◽

Structural Parameters ◽

Exact Methods ◽

Fixed Parameter Tractable ◽

Computational Costs ◽

Fixed Parameter ◽

Account Information ◽

The Given ◽

Theoretical Results

Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in polynomial time. However, here the order of the polynomial in the running time depends on the width, and this is known to be unavoidable; therefore, the problem is not fixed-parameter tractable parameterized by either of these width measures. Here we introduce an enhancement of tree and hypertree width through a novel notion of thresholds, allowing the associated decompositions to take into account information about the computational costs associated with solving the given CSP instance. Aside from introducing these notions, we obtain efficient theoretical as well as empirical algorithms for computing threshold treewidth and hypertree width and show that these parameters give rise to fixed-parameter algorithms for CSP as well as other, more general problems. We complement our theoretical results with experimental evaluations in terms of heuristics as well as exact methods based on SAT/SMT encodings.

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