Testimonials

“It is believed that the quantitative science of probability emerged after a famous gambler, Chevalier de Méré, posed to his friend Blaise Pascal the problem of distributing the gains between the players in an interrupted game of dice. Méré, a very skilled gambler, was famous for instinctively evaluating the advantage of a player in what would have involved, quantitatively, the computation of the odds down to the fourth decimal. The modern theory of probability has progressed considerably beyond the probability distributions of Chevalier de Méré, of course, and no one today would trust a gambler’s intuition over the ruling of the computer. Ed Thorpe, the father of quantitative finance and the founder of the first quantitative hedge fund, is famous for writing a computer program and for no longer relying on human instinct, when he set out to beat the casino at the game of Black Jack, and subsequently to beat the market at the game of option pricing. In fact, Ed Thorp had discovered and programmed an ancestor version of the Black and Scholes formula.

Option pricing and trading, however, do not fall under probability theory, but go beyond it. The very existence of a market is a direct argument against any attempt to run a computer program to compute the odds. Indeed, it is precisely the job of the option trader to trade the option at a price that will be different from the computer’s prediction. For how else to make money and how even to have a market? This problem, or paradox, is constitutive of the derivatives market, and is known as the ‘smile problem’. I have personally written two books, precisely to show how it can (and must) be addressed outside probability (the subtitle of The Blank Swan, the first book I wrote, is The End of Probability).

My encounter with Brad was key in both my endeavours, as a writer and technology provider. The Black and Scholes model of constant volatility is long surpassed. The consisting pricing of derivatives today requires stochastic volatility and jumps in the underlying. But none of these complex probability distributions could be determined and used in a computer program if an experienced option trader, like Brad, were not able to feed the computer with his intuition of the volatility smile, or in other words, with his exact assessment of the dearness of out-of-the money option relative to the at-the-money options, or to the Black and Sholes hypothesis of a single volatility number. A modern derivative pricing model is only as good as its capacity to be constantly re-calibrated against new option prices, and these, contrary to the days of Méré or indeed Thorp, can only be set by a skilled trader. The derivative pricing technology is only here to guarantee the consistency between the derivatives prices. But it is up to the trader to push into the model the main pivot points of the volatility surface.

I owe to Brad to have been the first option trader to contact me (in 2008). Today our derivative pricing technology and handling of the volatility smile is the most advanced there is, and it is in no small measure that we owe to Brad’s constant feedback, the major advances that we have accomplished over our eight-year collaboration. Brad has also left on me his personal mark as a friend and inspirer of my most penetrating thoughts relative to the volatility smile and to the metaphysics of the derivative market. This is apparent in the third part of my book, The Blank Swan, by far the most important part, which recounts the significance of my ‘flight to Sydney’ and the potential revolution of my thought and my world that this has brought about.”