Click to increase image sizeClick decrease size AcknowledgmentsBruno Dupire, Emanuel Derman, Jean-Philippe Bouchaud, Elie Canetti, Marco Avellaneda, Michal Kolano, IMF Staff. JP Morgan, New York, June 16, 2011; CFM, Paris, 17, GAIM Conference, Monaco, 21, Max Planck Institute, Berlin, 23, Eighth International Conference on Complex Systems, Boston, July 1, 2011, Columbia University September 24, 2011.

The impact of increasing leverage in the economy produces hyperreaction market participants to variations their revenues. If income banks decreases, they mass-reduce lendings; if corporations sales drop, and cannot adjust liquidities by further borrowing due existing debt, then must immediately reduce expenses, lay off staff, cancel investments. This a bifurcation mechanism, eventually strong dynamical instability capital markets that is commonly called systemic risk. In this article, we...

We present a non-naive version of the Precautionary (PP) that allows us to avoid paranoia and paralysis by confining precaution specific domains problems. PP is intended deal with uncertainty risk in cases where absence evidence incompleteness scientific knowledge carries profound implications presence risks "black swans", unforeseen unforeseable events extreme consequence. formalize PP, placing it within statistical probabilistic structure ruin problems, which system at total failure, place...

This paper presents a novel approach to financial network analysis by leveraging PolyModel theory. Traditional networks often rely on correlation matrices represent relationships between assets, but these fail capture the complex, non-linear interactions prevalent in markets. In response, we propose method that quantifies relationship time series comparing their reactions broad set of environmental risk factors. constructs based inherent similarities how assets respond external risks,...

For a Brownian motion $B=(B_t)_{t\le 1}$ with $B_0=0$, {\bf E}$B_t=0$, E}$B_t^2=t$ problems of probability distributions and their characteristics are considered for the variables $$ \begin{array}{c} {\mathbb D} =\displaystyle\sup_{0\le t\le t'\le 1}(B_t-B_{t'}),\qquad D}_1=B_\sigma-\inf_{\sigma\le 1}B_{t'}, \\ D}_2=\displaystyle\sup_{0\le t\le\sigma'}B_{t}-B_{\sigma'}, \end{array} where $\sigma$ $\sigma'$ times (non-Markov) absolute maximum minimum on $[0,1]$ (i.e., $B_\sigma=\sup_{0\le...

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We first recall the well-known expression of price barrier options, and compute double options by mean iterated mirror principle. The formula for barriers provides an intraday volatility estimator from information high-low-close prices. Then we give explicit formulas probability distribution function expectation exit time single options. These allow to independent dependent rebates. They are also helpful hedge when taking into account variations term structure interest rates volatility....

The aim of this work is to build a class financial crisis indicators based on the spectral properties dynamics market data. After choosing an appropriate size for rolling window, historical data inside window are seen every trading day as random matrix from which correlation obtained. Our goal study correlations between assets that constitute and look reproducible patterns indicative impending crisis. A weighting in then introduced proportional daily traded volumes. This manipulation...

The 2007-2009 financial crisis provided need to investigate the causes of systemic risk - also known as contagion and cures avoid it. In this article, we use well-established theories in dynamical systems, bifurcation, symbolic dynamics, chaos, explain mechanism behind crisis, provide insight on why conventional economic stimulus including quantitative easing cannot improve sluggish economy resolve liquidity shortage well expected. We further suggest how future should be executed, whether...

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The global financial market has become extremely interconnected as it demonstrates strong nonlinear contagion in times of crisis. As a result, is necessary to measure systemic risk comprehensive and approach. By establishing large set factors the main bones network applying factor analysis form so-called PolyModel, this paper proposes two indicators that can prognosticate advent trace development crises. Through analysis, theoretical simulation, empirical data final validation, we argue...