The Black Swan: The Impact of the Highly Improbable

Double bubble:the problem of derivatives is that if the underlying security has mild fat tails and follows a mild power law (i.e., a tail exponent of three or higher), the derivative will produce far fatter tails (if the payoff is in squares, then the tail exponent of the derivatives portfolio will be half that of the primitive). This makes the Black-Scholes-Merton equation twice as unfit!

Poissonbusting:the best way to figure out the problems of the Poisson as a substitute for a scalable is to calibrate a Poisson and compute the errors out of sample. The same applies to methods such as GARCH—they fare well in sample, but horribly, horribly outside (even a trailing three-month past historical volatility or mean deviation will outperform a GARCH of higher orders).

Why the Nobel:derman and Taleb (2005), Haug (2007).

Claude Bernard and experimental medicine:“Empiricismpour le présent, avecdirection a aspirationscientifique pour Vavenir.” From Claude Bernard, Principede la médecine expérimentale. See also Fagot-Largeault (2002) and Ruffle (1977). Modern evidence-based medicine: Ierodiakonou and Vandenbroucke (1993) and Vandenbroucke (1996) discuss a stochastic approach to medicine.

CHAPTER 19

Popper quote:from Conjectures and Refutations, pages 95-97.

The lottery paradox:this is one example of scholars not understanding the high-impact rare event. There is a well-known philosophical conundrum called the “lottery paradox,” originally posed by the logician Henry Kyburg (see Rescher [2001] and Clark [2002]), which goes as follows: “I do not believe that any ticket will win the lottery, but I do believe that all tickets will win the lottery.” To me (and a regular person) this statement does not seem to have anything strange in it. Yet for an academic philosopher trained in classical logic, this is a paradox. But it is only so if one tries to squeeze probability statements into commonly used logic that dates from Aristotle and is all or nothing. An all or nothing acceptance and rejection (“I believe” or “I do not believe”) is inadequate with the highly improbable. We need shades of belief, degrees of faith you have in a statement other than 100% or 0%.

One final philosophical consideration. For my friend the options trader and Talmudic scholar Rabbi Tony Glickman: life is convex and to be seen as a series of derivatives. Simply put, when you cut the negative exposure, you limit your vulnerability to unknowledge, Taleb (2005).

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