The Linda Problem of Kahneman and Tversky:
In the Linda Problem, one is given characterological info about Linda's feminist liberal history, and then asked: which is more likely: Linda is a bank teller or Linda is a bank teller with an interest in the feminist movement.
1/n ...
The "correct" answer is to think ensemble-wise, and say that yes, it's obvious that there are less feminist bank tellers than bank tellers. But many people give the other answer, that it's more likely that Linda is a feminist bank teller.
2/n ...

So here's the story: my son and I went to see Oppenheimer and were distinctly underwhelmed. (And IMO there was much too much dramatic music)

1/n But let me tell you some extremely extremely barely visible link I have to some character there. I was at Columbia as a grad student in the early 70s. Robert Serber, who was one of Oppenheimer's students, taught us quantum mechanics.
2/n

"A Stylized History of Volatility" -- to appear in FINANCE AND SOCIETY VOLUME 9, ISSUE 1, JUNE 2023
_________
Volatility is the propensity to continually change one’s current state, irrespective of the direction of the change …

papers.ssrn.com/sol3/papers.cf… 1/n This paper is a long history of volatility modeling in finance, with explanatory semi-technical details and lots of figures about Brownian motion etc, for non finance people, cultural anthropologists, sociologists, etc. ...

A thread on omething interesting about the belief in the reality of atoms and molecules that I sort of dug up today:

1/n In the nineteenth century people understood from chemistry that compounds behaved as though they combined from definite integer amounts of their constituents, suggesting the existence of molecules and atoms. (en.wikipedia.org/wiki/Gay-Lussa…)

2/n

A short thread about the Black derivation of Black-Scholes
________________
I first learned the Merton derivation of BS, pretty much the standard one now. You hedge the option with delta shares, find delta to make the portfolio riskless, then it must earn the riskless return
1/n …
That pde, using stochastic calculus, gives you the BS pde. In my youth I liked that precise argument. And when I learned that derivation I didn’t even know what CAPM was, and when I learned it I was unimpressed.
BUT …
2/n

A short thread about GameStop and Populism and The Central Dogma of Derivatives.

The “populist” nature of the r/WSB pumping of GameStop that required SAC and Citadel “experts” to rescue Melvin Capital “experts” after the attack by the financial non-elite isn’t completely new.
1/ In the 1980s LOR used Black-Scholes expertise to bring dynamic portfolio “hedging” to the masses with well-known consequences.

In the early 2000s the rise of CDS made it easy to trade credit, formerly the domain of experts too.
2/

Financial scam history for those interested in both scams and accrued interest:
In the early 80s Drysdale Securities went bust and caused a loss for Chase, their agent, of tens to hundreds of millions and almost brought them down.
1/n As large rates were coming down, Drysdale lost money on their bets. They hid them by borrowing high coupon Treasuries, and putting up only the flat price without accrued interest, which for high coupons in those days was large.
2/n

The implied volatility of an option represents two ideas:

1a. It is the lognormal volatility the underlier would have to have in the future to expiration if the underlier evolved by geometric Brownian motion;

and …

1/n …
1b. you were able to replicate the option a la Black-Scholes by continuous delta-hedging with no transactions costs etc;

and

2. The implied volatility is also overlaid with another component that represents demand and supply for the option itself.

…

2/n

So for many years we have been taught by mavens and had it parroted to us by many followers that we don’t understand obscurely phrased statistical paradoxes in unrealistic cases where we pretend the exact statistics are known. (They never are IRL)

1/2 What we should have been taught was not statistical analysis but scenario analysis. Good financial risk managers look at probabilistic models but know that there are certain scenarios where you ignore probability and make sure you’re not exposed to them.
2/2

So, let me get back to science and even statistics about volatility, for your amusement and even edification.

If you look at S&P implied volatility over the last week or so, here is the well-known rule that seems to be holding:
1/n ... …
Observe the at-the-money S&P implied volatility skew w.r.t strike each evening. Call it X vol points per S&P strike point.
Then, the night night, look at how much at-the-money implied volatility changed as the S&P level changed.

2/n ...