The History of the Black-Scholes Formula

LTCM's problem wasn't anything to do with the Black-Scholes model. In fact far from it, LTCM's market risk management was very good (for its time).

Where they became unstuck was in liquidity and capital risk management. Where the banks got unstuck wrt LTCM was in credit risk management.

Where the banks didn't learn the lessons of LTCM was in them still not being good enough at liquidity and capital risk management come 2008.

And one more tangential point as I see this reasonably regularly. The key insight from Black-Scholes isn't the use of normal vols. It was known pretty much straight away that a lot of market where it was used weren't normal (in the probabilistic sense).

The key insight was to use the no arbitrage concept for pricing derivatives. This was and is a hugely powerful tool and was an asset to financial management (excuse the pun).

First of all, the vast majority of LTCM's trades had nothing at all to do with the Black-Scholes-Merton formula (BSM). They were just highly levered mean reversion trades. The fall of LTCM had nothing to do with the BSM formula, it had everything to do with leverage.

Secondly, vanilla BSM with constant volatility isn't really used to do anything important anymore. It was going away much earlier than 1997 anyway; the Heston model came around in 1993, and Derman was using a primitive version of local vol around the same time. And of course people knew that financial asset returns were not normally distributed with constant vol (Mandelbrot wrote a paper describing that in 1963!).

I won't even get into why his (and Salmon's) description of how the Li formula was used is completely wrong.

http://www.amazon.com/Inventing-Money-Long-Term-Capital-Mana...

Most people read this book but I think the above book is much better.

http://www.amazon.com/When-Genius-Failed-Long-Term-Managemen...

I'd recommend reading both if this sort of thing interests you, in the order that they are listed.

Since this article is mostly about LTCM, its kindof interesting to look at their downfall and realize that in the end they were right, their trades ended up being profitable, they were just so leveraged that when the markets started to diverge they couldn't make their margin calls.

Interestingly the reason things went south so fast was that LTCM and the banks had different risk models.

To LTCM they would do spread trades, where you take 2 very similar instruments, the article mentions 29.5 and 30 year bonds. You short the one you think is expensive and buy the one you think is cheap and hold them until the prices converge.

This has a nice risk management feature that the risk on both cancel each other out almost as if the markets move up, your long leg covers the loss on your short leg and visa versa if markets move down.

Unfortunately, partially due to secrecy(trying to hide what they were doing) and partially due to just who had the bond inventory to short from, they often ended up having the long leg and the sort leg at two different banks.

So to LTCM they were perfectly hedged, while to the bank with the short positions, if the market went up they needed LTCM to send them more margin. So LTCM, which was already heavily leveraged was required to send their prime brokers margin that they never figured they'd need to.

Couple that with markets that started move in an unprecedented manner caused too many of their spreads to diverge beyond what they could cover.

The firm ends up getting a margin call it can't afford, liquidates everything to its prime brokers and other investment banks and those banks end up making money off their trades in a time frame from 6 months (for Goldman) to 3 years for the longer term bonds.

Even when your models are right the market can still rip you to shreds:(

EDIT As to book recommendations below is a picture of my work bookshelf. Id' recommend most of the books on the shelf: https://imgur.com/OdzB4aW

https://imgur.com/zdLSEek

LTCM's problem wasn't the BSM per-se, it was the fact that they went chasing after trading opportunities once the arbitrage space in bond/swap spreads had been, ironically, arbitraged away. In the process of doing this they leveraged themselves to the hilt and basically ran out of cash defending the positions.

What calculators would that be in the late Seventies?