Elie Ayache’s synopsis of The Blank Swan
I guess my whole point about probability is that it is a contingent concept and hence can be replaced (it is historically dated). Its main weakness is the identification and delimitation of states of the world to which the probability distribution applies. In case of roulette, or dice, or marbles in a jar, this is not a problem as the possible states (or draws) are clearly defined. In “massive reality”, however, or in the market (which is also a massive reality), it is not so clear that it is even legitimate to discern and identify possible states.
For instance, you are tempted to identify the prices of the option’s underlying as only states, however, the mere fact that options trade in their own market leads to you to also “sample” different volatility levels as other states; this, in turn, is not enough because barrier options (or exotic options of payoffs more complex than the vanillas) also simultaneously trade independently of the vanillas and their prices may not be explainable except in an even higher-level model where not only volatility is stochastic but its own volatility is stochastic, etc.
In sum, if we define a market (of contingent claims) as a place where contingent claims of every level of complexity trade simultaneously, at prices that are not redundant which each other, then you will find that you can never capture this in a picture with defined states. People commonly think that there is such a picture, only it changes and expands over time. This is exactly what I dispute, for, in my mind, the definition of market is instantaneous (all contingent claims must instantly trade non redundantly).
The more I thought about this problem, the more it appeared to me that the picture (contingent claims, prices) should completely replace the traditional picture (states of the world, probabilities). Think of the market (or at least, of an idealized picture thereof such as I offer in the book) as a whole new logic, which replaces the logic of probability. Instead of abstract metaphysical states, let us adopt written and material contingent claims. Instead of probability trees and probabilistic transitions, let us adopt the massive exchange place and the coexistence of all prices.
As a matter of fact, derivatives practitioners very commonly “infer” the stochastic process of the underlying from the instant constellation of prices of its derivatives. They very seldom try to infer it from the history of prices of the underlying! My whole philosophy is to try to radicalise this alternative and to no longer believe in temporal processes (or generally in probability) but only in markets and prices.