Poly%20Lecture%203 - Risk Management in the Real World...

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Risk Management in the Real World Lecture 3 More on Fat Tails and Power Laws
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N N Taleb © 2008 Not Very Funny! 2
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Derivatives • They pay in square ---typically • Variance swaps depend on E[X 2 ] N N Taleb © 2008 3
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N N Taleb © 2008 Grass Not trees 4
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N N Taleb © 2008 5
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N N Taleb © 2008 6
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N N Taleb © 2008 Stopping Time 7
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Stable Distribution For an introduction: • Wikipedia is (as of March 2) correct http://academic2.american.edu/ ~jpnolan/stable/chap1.pdf N N Taleb © 2008 8
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Pareto-Levy-Mandelbrot • IId • Basin of Attraction • Triplet (sigma, beta,mu)
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Three Parameters
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Levi process alpha=2
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Levi process alpha =1.99 -100 -50 0 10000 20000 30000 40000 50000
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Switch to the tail A Power law starts “in the tail” Where is the tail? You need to know the exponent to know where the tail is ….and you need to know the tail to know the exponent Do not confuse Levi-alpha with PL alpha (physicists call it mu)
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Not too fast: • Speed of Convergence is slow for power laws (even if second moment is Fnite)
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Student T
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N N Taleb © 2008 Convergence to a Gaussian Moments are defned up to the alpha Convergence can be slow, very slow… 16
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N N Taleb © 2008 The center is where the action is 17
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N N Taleb © 2008 Convergence 18
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N N Taleb © 2008 Ito’s Lemma with a Finite Variance --but Scalable 19
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Inverse Problems N N Taleb © 2008 20
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Student /Lognormal N N Taleb © 2008 21
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Poly%20Lecture%203 - Risk Management in the Real World...

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