Raphael Douady

by Nassim Nicholas Taleb and Raphael Douady

Using the metadistribution of possible distributions for a given measure, we define a condition u... more Using the metadistribution of possible distributions for a given measure, we define a condition under which it is possible to make a decision based on the observation of random variable, which we call "statistical decidability".
We provide a sufficient condition on the metadistribution for the decision to be "statistically decidable" and conjec- ture that decisions based on a metadistribution with non compact support are always "statistically undecidable".

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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

HAL (Le Centre pour la Communication Scientifique Directe), Aug 6, 2012

We provide a mathematical definition of fragility and antifragility as negative or positive sensi... more We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it improves on stress testing and bypasses the common flaws in Value-at-Risk.

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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

RePEc: Research Papers in Economics, 2013

We provide a mathematical definition of fragility and antifragility as negative or positive sensi... more We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk. What is Fragility? The notions of fragility and antifragility were introduced in Taleb(2011,2012). In short, fragility is related to how a system suffers from the variability of its environment beyond a certain preset threshold (when threshold is K, it is called K-fragility), while antifragility refers to when it benefits from this variability-in a similar way to "vega" of an option or a nonlinear payoff, that is, its sensitivity to volatility or some similar measure of scale of a distribution. Simply, a coffee cup on a table suffers more from large deviations than from the cumulative effect of some shocks-conditional on being unbroken, it has to suffer more from "tail" events than regular ones around the center of the distribution, the "at the money" category. This is the case of elements of nature that have survived: conditional on being in existence, then the class of events around the mean should matter considerably less than tail events, particularly when the probabilities decline faster than the inverse of the harm, which is the case of all used monomodal probability distributions. Further, what has exposure to tail events suffers from uncertainty; typically, when systems-a building, a bridge, a nuclear plant, an airplane, or a bank balance sheet-are made robust to a certain level of variability and stress but may fail or collapse if this level is exceeded, then they are particularly fragile to uncertainty about the distribution of the stressor, hence to model error, as this uncertainty increases the probability of dipping below the robustness level, bringing a higher probability of collapse. In the opposite case, the natural selection of an evolutionary process is particularly antifragile, indeed, a more volatile environment increases the survival rate of robust species and eliminates those whose superiority over other species is highly dependent on environmental parameters.

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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

arXiv (Cornell University), Aug 6, 2012

We provide a mathematical definition of fragility and antifragility as negative or positive sensi... more We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk. What is Fragility? The notions of fragility and antifragility were introduced in Taleb(2011,2012). In short, fragility is related to how a system suffers from the variability of its environment beyond a certain preset threshold (when threshold is K, it is called K-fragility), while antifragility refers to when it benefits from this variability-in a similar way to "vega" of an option or a nonlinear payoff, that is, its sensitivity to volatility or some similar measure of scale of a distribution. Simply, a coffee cup on a table suffers more from large deviations than from the cumulative effect of some shocks-conditional on being unbroken, it has to suffer more from "tail" events than regular ones around the center of the distribution, the "at the money" category. This is the case of elements of nature that have survived: conditional on being in existence, then the class of events around the mean should matter considerably less than tail events, particularly when the probabilities decline faster than the inverse of the harm, which is the case of all used monomodal probability distributions. Further, what has exposure to tail events suffers from uncertainty; typically, when systems-a building, a bridge, a nuclear plant, an airplane, or a bank balance sheet-are made robust to a certain level of variability and stress but may fail or collapse if this level is exceeded, then they are particularly fragile to uncertainty about the distribution of the stressor, hence to model error, as this uncertainty increases the probability of dipping below the robustness level, bringing a higher probability of collapse. In the opposite case, the natural selection of an evolutionary process is particularly antifragile, indeed, a more volatile environment increases the survival rate of robust species and eliminates those whose superiority over other species is highly dependent on environmental parameters.

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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

Oxford University Press eBooks, Sep 29, 2016

We provide a mathematical definition of fragility and antifragility as negative or positive sensi... more We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it improves on stress testing and bypasses the common flaws in Value-at-Risk.

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Tempered Stable Processes with Time Varying Exponential Tails

HAL (Le Centre pour la Communication Scientifique Directe), Jun 13, 2020

In this paper, we introduce a new time series model having a stochastic exponential tail. This mo... more In this paper, we introduce a new time series model having a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. The model captures the stochastic exponential tail, which generates the volatility smile effect and volatility term structure in option pricing. Moreover, the model describes the time-varying volatility of volatility. We empirically show the stochastic skewness and stochastic kurtosis by applying the model to analyze S\&P 500 index return data. We present the Monte-Carlo simulation technique for the parameter calibration of the model for the S\&P 500 option prices. We can see that the stochastic exponential tail makes the model better to analyze the market option prices by the calibration.

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The StressVaR: A New Risk Concept for Extreme Risk and Fund Allocation

The Journal of Alternative Investments, Dec 31, 2010

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Yield Curve Smoothing and Residual Variance of Fixed Income Positions

Social Science Research Network, 2001

We model the yield curve in any given country as an object lying in an in…nite-dimensional Hilber... more We model the yield curve in any given country as an object lying in an in…nite-dimensional Hilbert space, the evolution of which is driven by what is known as a cylindrical Brownian motion. We assume that volatilities and correlations do not depend on rates (which hence are Gaussian). We prove that a principal component analysis (PCA) can be made. These components are called eigenmodes or principal deformations of the yield curve in this space. We then proceed to provide the best approximation of the curve evolution by a Gaussian Heath-Jarrow-Morton model that has a given …nite number of factors. Finally, we describe a method, based on …nite elements, to compute the eigenmodes using historical interest rate data series and show how it can be used to compute approximate hedges which optimise a criterion depending on transaction costs and residual variance. Dedication A …rst version of this article was written in 1994, while the author was working Société Générale in the …xed income and FX derivatives trading room (this version has been …nalized in 2001, but was never published before). This work raised the interest of Marek Musiela, who at that time was teaching at the University of New Sounth Wales in Sydney, and was at the origin of the long and fructful scienti…c relationship between the author and Marek Musiela. It is therefore the author's pleasure to dedicate this article to him, as a testimony of friendship and admiration.

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An empirical approach to financial crisis indicators based on random matrices

RePEc: Research Papers in Economics, Jun 1, 2015

The aim of this work is to build financial crisis indicators based on spectral properties of the ... more The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtained. The financial crisis indicators that we have built deal with the spectral properties of these covariance and correlation matrices and they are of two kinds. The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix representing either a calm or agitated market. The idea behind this first type of indicators is that when the empirical distribution of the spectrum of the covariance matrix is deviating from the reference in the sense of Hellinger, then a crisis may be forthcoming. The second type of indicators is based on the study of the spectral radius and the trace of the covariance and correlation matrices as a mean to directly study the volatility and correlations inside the market. The idea behind the second type of indicators is the fact that large eigenvalues are a sign of dynamic instability. The predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective-put strategy.

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Genetic Algorithm-Based Combination of Predictions

Springer eBooks, 2022

Predictions of Market Returns

Springer eBooks, 2022

Predictions of Specific Returns

Springer eBooks, 2022

Predictions of Industry Returns

Springer eBooks, 2022

Artificial Intelligence for Financial Markets

Springer eBooks, 2022

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more

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Estimation Method: The Linear Non-Linear Mixed Model

Springer eBooks, 2022

Polymodel Theory: An Overview

Springer eBooks, 2022

Mathematical Definition, Mapping, and Detection of (Anti)Fragility

Social Science Research Network, 2012

We provide a mathematical definition of fragility and antifragility as negative or positive sensi... more We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk. What is Fragility? The notions of fragility and antifragility were introduced in Taleb(2011,2012). In short, fragility is related to how a system suffers from the variability of its environment beyond a certain preset threshold (when threshold is K, it is called K-fragility), while antifragility refers to when it benefits from this variability-in a similar way to "vega" of an option or a nonlinear payoff, that is, its sensitivity to volatility or some similar measure of scale of a distribution. Simply, a coffee cup on a table suffers more from large deviations than from the cumulative effect of some shocks-conditional on being unbroken, it has to suffer more from "tail" events than regular ones around the center of the distribution, the "at the money" category. This is the case of elements of nature that have survived: conditional on being in existence, then the class of events around the mean should matter considerably less than tail events, particularly when the probabilities decline faster than the inverse of the harm, which is the case of all used monomodal probability distributions. Further, what has exposure to tail events suffers from uncertainty; typically, when systems-a building, a bridge, a nuclear plant, an airplane, or a bank balance sheet-are made robust to a certain level of variability and stress but may fail or collapse if this level is exceeded, then they are particularly fragile to uncertainty about the distribution of the stressor, hence to model error, as this uncertainty increases the probability of dipping below the robustness level, bringing a higher probability of collapse. In the opposite case, the natural selection of an evolutionary process is particularly antifragile, indeed, a more volatile environment increases the survival rate of robust species and eliminates those whose superiority over other species is highly dependent on environmental parameters.

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Statistical Undecidability

Social Science Research Network, 2010

Using the metadistribution of possible distributions for a given measure, we define a condition u... more Using the metadistribution of possible distributions for a given measure, we define a condition under which it is possible to make a decision based on the observation of random variable, which we call "statistical decidability". We provide a sufficient condition on the metadistribution ...

On the super-additivity and estimation biases of quantile contributions

Physica D: Nonlinear Phenomena, Jul 1, 2015

Sample measures of top centile contributions to the total (concentration) are downward biased, un... more Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A ∪ B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.

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Bermudan Option Pricing with Monte-Carlo Methods

WORLD SCIENTIFIC eBooks, 2002

We explain, compare and improve two algorithms to compute American or Bermudan options by Monte-C... more We explain, compare and improve two algorithms to compute American or Bermudan options by Monte-Carlo. The …rst one is based on threshold optimisation in the exercise strategy (Andersen 1999). The notion of "fuzzy threshold"is introduced to ease optimisation. The second one uses a linear regression to get an estimate of the option price at intermediary dates and determine the exercise strategy (Carriere 1997, Longsta¤-Schwartz 1999). We thoroughly study the convergence of these two approaches, including a mixture of both.

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