There used to be two schools of thought about the causes of the 2008 financial crisis. The one the wonks were circling around was "we never should have let all these investment firms come up with these crazy-exotic models of money flow and investment risk because they traded models of the models of the models and the whole world blew up." The one the bros were circling around was "nobody could have seen that coming, d00d." Then Michael Lewis wrote The Big Short and the narrative became "nobody could have seen that coming - except my plucky heroes, d00d!"

I lead with this because "except my plucky heroes" is basic narrative storytelling whereas "we should have leashed our wizards" is advanced narrative storytelling. Basic storytelling is necessary to get the point across to The Stupids. Advanced storytelling might actually change things. The basic storytelling allows most of the world to go "well I guess that'll never happen again, good thing they fixed it" while the advanced storytelling, unobserved by nearly everyone, made it hella harder for super-crazy-hyperexotic math to break the world.

And by "super-crazy-hyperexotic math" we might be talking about diff EQ? Because the finance world sucks at math. See this thing? they gave it a Nobel Prize in Economics (which is not a Nobel and never will be) and it's literally "price over earnings times a seasonal coefficient." Which means anybody who can use an equation with an integral in it is a quant. And you don't get to go drinkin' with the boys on Tuesdays if you talk to the quants. Their job is to give us stuff to bet on. I mean sell to investors.

(I'm getting there I promise)

Buried hyper-deep in books that nobody recommends anymore is this very simple fact:

AIG built a model that told them that the odds of housing prices in the United States dropping by an aggregate of more than five percent was a "six sigma event" and described them as such. This makes them sound like they've been reading Taleb. What Taleb meant was "six or more standard deviations away from the mean" but what Taleb really meant was "nobody could have seen that coming, d00d." Taleb starts Black Swan with the assertion that nobody could have predicted Hitler, despite both Churchill and Wilson expressly predicting Hitler at the Treaty of Versailles, in public speeches.

This only matters because AIG used that model to insure the policies of Goldman Sachs, Chase, Washington Mutual, Bear Stearns and all the rest. And those policies underwrote their risk of mortgages going bad. And the riskier those mortgages were, the more of a premium those bonds paid to the bondholders. And the more the premium paid, the more money everyone made. Including AIG.

Who argued, based on fuckall, that the sun was more likely to go nova in 2009 than that housing prices would dip 5%.

NOW

I would argue that not a single "quant" argued that a housing dip was less likely than the sun going nova. But a whole lotta quants put together position papers and equations and arguments and justifications for finance bros to blast clear through any safeguards or lending requirements. What's the Mencken quote that was actually Upton SInclair? “It is difficult to get a man to understand something, when his salary depends upon his not understanding it!” Mencken gets credit because Paul Krugman credited him erroneously in 1989. Krugman went on to win the Nobel Prize in Economics.

So the problem you will encounter is that the smarter you are, the better you are with numbers, the more easily you can manipulate them, the more likely you are to be asked to lie with them. The finance industry uses math the way RFK uses science - they cherry-pick stuff they don't understand to sell to gullible regulators who already want to believe. The actual money-making portion of the program is back-room deals and insider trading.

The "mathiness" portion of this debacle began with LTCM in 1998. Timeline goes like this:

- 1994: John Merriweather builds a magic new math fund around Myron Scholes' risk model

- 1997: Myron Scholes wins the Nobel Prize in Economics

- 1998: LTCM loses $5b for not predicting that the collapse of the Soviet Union would be economically spicy

When Genius Failed is a good book about that.

Fast forward ten years and everyone who made fun of LTCM (their approach was mocked as "picking up nickels in front of steamrollers") is now discovering the profits to be made if you adopt a Schroedinger's Risk model: things are very risky when making money off them, not risky at all when you're insuring against them. There are dozens of books about what happened next, just watch this instead.

And yes, none of this is relevant to your actual request, which is "how do I do math stuff with finance" and that's not me changing the subject or evading, because the math stuff is all delta gamma zeta options bullshit which isn't really math, it's Advanced Gambling. The book I recommend on finance is A Random Walk Down Wall Street which is now fifty fucking years old but gets to the basics in an extremely accessible way. Here are my caveats:

1) It pretends that markets are perfectly efficient when it's thunderously obvious that they work by insider trading and informational advantage

2) It argues that you make more money by staying in the market at all times rather than admitting that knowing when to fucking bail is a more effective strategy

3) It basically says "don't" about options and exotic mathematical instruments because fucking hell in 1973 John Merriweather was a fresh MBA in the pit at Salomon

Michael Lewis chose Michael Burry as his hero for The Big Short because Michael Burry, autist, went through and read the prospectii of all these credit default swaps and went "wait a minute... this shit only works if the housing market doesn't drop more than five percent!" he was also monied enough that he could go to Goldman Sachs and say "I would like to bet against you, create a credit default swap that pays out when the rest of your shit goes into default and sell it to me." He then got Goldman Sachs to grudgingly pay out after they initially ruled that they didn't have to because the only person who bought this CDO was Michael Burry. I mention this because "it's stupid to presume that the sun is more likely to go nova than for housing prices to drop five percent" isn't arcane knowledge. It's fucking obvious. But the whole "quant" universe of finance is about burying obvious truths in illegible equations so that you can sell them to pension funds.

Now get back to me once you can keep down some apple sauce and oatmeal and we'll continue the purge.