Nassim Nicholas Taleb’s Quantitative Notes & Lectures

 

 

 

 

 

A mixture of my lectures at the Courant Institute, & musings when I am bored, ranging from probability theory & quantitative finance to computational epistemology.

 

Technical Paper on Fat Tails, or Why the Lévy Regime does not count  MY CENTRAL PAPER [Everything is there –why option pricing is done by expectations of conditional mean, why variance is for the morons, etc.]

 

 

         PREASYMPTOTICS, INVERSE  PROBLEMS, AND PLATONICITIES: LECTURES ON RISK & PROBABILITY

 

Aims of the lectures:

In short, statistics without being an idiot savant.

·      Pre-asymptotics (all that happens takes place outside the limit),

·      Inverse Problems (many models can explain the same phenomena), and

·      Platonicities (the reduction of the fool) 

are the same illness under different symptoms.
Probability theory does not have to be Platonic. It can use mathematical tools without being overly theoretical, or naively theoretical (bogus essentialism).

You can go from empiricism to formalism --looking for inverse problems and sensitivity to error in the choice of model.

 

Lecture 1 – Platonic convergence & the Central Limit Theorem.

 

Lecture 2 - Preasymptotics & Small Sample Effects of  α≤1 or Saint Petersburgh-Style Infinite First Moment Situations.

 

Lecture 3 - The fundamental problem of the 0th  moment and the irrelevance of "naked probability"

 

Lecture 4 - An epistemological derivation of power laws - The a Priori Problem of Small Probabilities . Summary of main idea on fat tails. Derive operational probability --in other words what you use in your decisions. "Beliefs" we will see do not count, but impact and payoffs.

 

Lecture 5 - How to Build a Poisson Buster – or why jump-diffusion is just ex-post fitting. Why  "Fat Tails" are not Poisson

 

Lecture 6 - Option Pricing & True Fat tails

 

Lecture 7- Small Probabilities & The Problem of Moral Hazard

 

Lecture 8 - L1 “Moments”

 

 

 

TECHNICAL BLOG on Wilmott.com –with quizzes. Raphael Douady and Bruno Dupire get things quickly. Quizzes 1 and 2 are here and here.

 

 

            MATHEMATICAL POINTS BURIED IN The Black Swan or Fooled by Randomness, & COURANT INSTITUTE CLASS NOTES & LECTURES

 

Why We Have Never Used the Black Scholes Merton Option Formula (with Espen Haug)

 

Reply to Statisticians on The Black Swan

 

 

Some economists making elementary confusions about inference.

           

 

NEW STUFF –After I switched to the Scalables
                       

The Tail Exponent MP3- NYU Courant Institute. Where I explain that a tail exponent for a derivatives portfolio is lower than that of the underlying; that the Central Limit Theorem only exists in Ecole Polytechnique (we never reach the asymptote in reality, which counts enormously for a scale-free distribution, even when the variance is finite); how to do a Poisson buster ( the Poisson distribution does not have scalable jumps).

 

 

Note with Benoit Mandelbrot on Pre-Asymptotics and Probability Distributions

 

Why Do People Like to Truncate the Upside? Call sellers fool themselves with the illusion of statistical properties       

 

Chapter on the Great Intellectual Fraud (GIF) (in The Black Swan)

 

 

 

OLD STUFF TWEAKING THE GAUSSIAN –much of it is just mathematical exercises that I hope are distribution-independent

 

The Dentist and His Emotions: The mathematics of the effect of narrow sampling period on one’s emotional well-being. [Application of Philostratus in Monte Carlo in FBR]

 

Path Dependent Survival : Monte Carlo Experiment With Path Dependence of Trader Survival Rates. Why path dependence makes a trader’s 5 year survival slim (only pancreatic cancer has better survival rates).

                       

Transaction Costs in the Literature  with some tweaking

 

Volatility Has a Natural Stochasticity to it even in the Gaussian Homoskedastic World   

 

Trading With a Stop in a Gaussian World

 

Dynamic Hedging and Volatility Expectation

 

Sigma-P or Volatility in Price Space

 

Option Replication and Transaction Costs

 

Introduction to Gambler’s Ruin

 

 

The Value-at-Risk Debate

I have always held that VAR is charlatanism, a dangerously misleading tool –like much of modern mathematized academic finance. These were my first forays against naive empiricism and the use of statistics in the social sciences. My language then was a bit primitive –the point was the same.

"The World According to Nassim Taleb" , the 5 page interview with Derivatives Strategy (January 1997) that started the debate. It is a non technical comment on the Value-at-Risk, statistical biases in traders' evaluations and the excesses of formalism in risk management. See Also "In Defense of VAR" , a reply by one Philippe Jorion, Professor of Finance at U.C. Irvine and author of Value-at-Risk (Irwin, 1996). Finally, my rebuttal "Against VAR", a methodological statement that summarizes my position against naive formalism and the raw application of engineering methods in risk management. I describe the risks of misspecification and warn against the primitive (and purely inductive methods) of frequency-based inference. In my answer to Philippe Jorion I explain in slightly more technical terms some of the statements made during my interview. Since then I stopped paying attention/partaking of these debates, particularly with untrained “risk experts ” unable to distinguish between skepticism and nihilism.