The Joint Distribution of Stock Returns Is Not Elliptical

Chicheportiche, Rémy; Bouchaud, Jean‐Philippe

doi:10.1142/s0219024912500197

Cited by 33 publications

(35 citation statements)

References 36 publications

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“…of parameters µ and N [26]. From a financial perspective, this parametrization can be useful as a model where all individual stock returns are impacted by the same, time dependent scale factor σ t that represents the "market volatility" (see [39] for a discussion of this assumption). From empirical studies, one possible choice that matches quite well the data is to choose Eq.…”

Section: B Free Multiplicative Noisementioning

confidence: 99%

Rotational Invariant Estimator for General Noisy Matrices

Bun

Allez

Bouchaud

et al. 2016

IEEE Trans. Inform. Theory

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108

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We investigate the problem of estimating a given real symmetric signal matrix C from a noisy observation matrix M in the limit of large dimension. We consider the case where the noisy measurement M comes either from an arbitrary additive or multiplicative rotational invariant perturbation. We establish, using the Replica method, the asymptotic global law estimate for three general classes of noisy matrices, significantly extending previously obtained results. We give exact results concerning the asymptotic deviations (called overlaps) of the perturbed eigenvectors away from the true ones, and we explain how to use these overlaps to "clean" the noisy eigenvalues of M. We provide some numerical checks for the different estimators proposed in this paper and we also make the connexion with some well known results of Bayesian statistics. arXiv:1502.06736v2 [cond-mat.stat-mech]

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Section: B Free Multiplicative Noisementioning

confidence: 99%

Rotational Invariant Estimator for General Noisy Matrices

Bun

Allez

Bouchaud

et al. 2016

IEEE Trans. Inform. Theory

Self Cite

108

View full text Add to dashboard Cite

show abstract

“…One of the most controversial assumptions in the portfolio theory is that returns are jointly normally distributed (or, at least, that the returns distribution is jointly elliptical). Some economist have pointed out the fact that this assumption might not capture well the reality of financial markets [14].…”

Section: Related Workmentioning

confidence: 99%

“…Gaussian mean approximation. Subplot a shows how the parameter α of the utility function should be chosen in function of the mean desired size of the coalitions (see equation14). Subplot b displays the corresponding utility functions for different values of α.…”

mentioning

confidence: 99%

Stability and Performance of Coalitions of Prosumers Through Diversification in the Smart Grid

Gensollen

Gauthier

Becker

et al. 2018

IEEE Trans. Smart Grid

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Abstract-Achieving a successful energetic transition through a smarter and greener electricity grid is a major goal for the 21st century. It is assumed that such smart grids will be characterized by bidirectional electricity flows coupled with the use of small renewable generators and a proper efficient information system. All these bricks might enable end users to take part in the grid stability by injecting power, or by shaping their consumption against financial compensation. In this paper, we propose an algorithm that forms coalitions of agents, called prosumers, that both produce and consume. It is designed to be used by aggregators that aim at selling the aggregated surplus of production of the prosumers they control. We rely on real weather data sampled across stations of a given territory in order to simulate realistic production and consumption patterns for each prosumer. This approach enables us to capture geographical correlations among the agents while preserving the diversity due to different behaviors. As aggregators are bound to the grid operator by a contract, they seek to maximize their offer while minimizing their risk. The proposed graph based algorithm takes the underlying correlation structure of the agents into account and outputs coalitions with both high productivity and low variability. We show then that the resulting diversified coalitions are able to generate higher benefits on a constrained energy market, and are more resilient to random failures of the agents.

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“…In particular, in Blattberg & Gonedes (1974) it was used for modeling stock dynamics, in Nadarajah et al (2015) for currencies, while Platen & Rendek (2008) have implemented it for modeling the returns of market indexes. Moreover, it was used for study of joint distribution by Chicheportiche & Bouchaud (2012) and it was obtained that it can provide a good fit for strongly correlated stocks. Since this function fits the historical observations of the log returns rather well, particularly at the tails, it has already found implementations for theoretical pricing of options.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Basnarkov

Stojkoski

Utkovski

et al. 2019

Int. J. Theor. Appl. Finan.

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A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student's t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter -the standard deviation of the Student's t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.

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The Joint Distribution of Stock Returns Is Not Elliptical

Cited by 33 publications

References 36 publications

Rotational Invariant Estimator for General Noisy Matrices

Rotational Invariant Estimator for General Noisy Matrices

Stability and Performance of Coalitions of Prosumers Through Diversification in the Smart Grid

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

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