Thread by @aubreyclayton

BTW, I worked my way through @nntaleb's paper so you don't have to. Unsurprisingly, it's garbage.
(cc: @NateSilver538)
drive.google.com/file/d/1tQj4ZG…

His main idea is that election forecast probabilities should be traded as option prices. This leads him to construct a stochastic process Y that these can be “derivatives” from, something like the vote-share in favor of a candidate.

Since he wants prices=probabilities, this makes him think that the process for Y must be a martingale, because he knows that in option-pricing you always change measure to the risk-neutral so that the underlying asset and option are both martingales. Thus, price=probability.

The problem is Y is bounded, which means it can’t be modeled by any of the standard martingales from quant finance. By making a clever choice, he finds a “shadow process” X and a transformation S such that Y = S(X), and X (Bachelier model) is something he can price with. Phew!

However, that’s all unnecessary because conditional probabilities are themselves always martingales by of the tower property of conditional expectation. One could start with any process for Y and compute conditional probabilities that Y(T) > threshold and get martingale prices.

He claims that any stochastic model for an underlying asset will produce binary option prices that converge to 0.5 as the volatility/uncertainty goes up. This is untrue.

For any given spot/strike combination, it’s true that option prices go to 0.5, but increasing the vol of Y also means you see more extreme spot prices.

E.g., here are paths of the forecast probabilities at time t for Y(T) > 1, for a Brownian motion with σ=1 and with σ=1000. See the difference? Exactly.

(That’s what we in the math business call a “whoopsie.”)

He claims his alternative model is better because it produces this behavior where every forecast is 50/50 up until the very last moment. Good luck with that.
And dear God this footnote:

.@nntaleb, if you’re reading this, the next time a poll in a two-candidate race shows one candidate at 10% and the other at 90%, I will gladly offer you 10-1 odds on the underdog for as much money as you want.

He also seems to misunderstand that the source of uncertainty in election forecasting isn’t just that people’s opinions will change but also that the opinions of the voting populace as a whole are unknown.

This means election forecasting isn’t like option pricing, where you have some observable security you’re writing derivatives on.

Basically the paper reads like what happens when someone who only thinks of probability in quant finance terms tries hard to make everything about quant finance. I will think a lot less of any journal that publishes it. /end