[zupatol]

The black-scholes model for pricing options had a big impact on the financial industry, and the big breakthrough for solving the equation was to realize it could be turned into the heat equation that already had a solution. If I remember well, the insight came to Robert Merton, an economist who had also studied engineering mathematics.

https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model

[calpaterson]

"Big impact" is understating it. It's caused at least one financial crisis when Scholes and Merton's hedge fund (https://en.wikipedia.org/wiki/Long-Term_Capital_Management) went boom in the late nineties.

Since then the assumptions present in Black-Scholes and similar pricing models have caused considerable chaos elsewhere in finance. One of those things that perhaps it would have been better that they had not invented. Professionally it was great for the inventors though: they won the Nobel Prize at the time.

[dkural]

The Ito calculus being applicable for solving Black-Scholes might be a better example for the original question :)

I am not sure it's better if that was not invented - the question of option pricing doesn't go away, it's a fundamental need for real businesses producing commodities that need to hedge real risk around the weather, or selling into cyclical industries etc.

LTCM (& it's failure) has as much to do with getting so big as to present a systemic risk to the entire financial sector, and over-leverage. No matter what formula they use to price their options, those two factors make for a dangerous combination. There is a perverse incentive to become "too big to fail", because if you truly reach that, the gains stay private whereas the losses are inevitably socialized to prevent taking down the whole system.

[ChrisLomont]

It's also led to lower costs in just about every industry due to the ability to price obscure contracts and lower risk. An example is airlines need to deal with fuel price volatility when selling tickets now, and, if they take on more risk, they need to price that into tickets. Getting someone to hedge against that lowers their risk. The pricing of such hedges and contracts has led to less volatility for pretty much every industry.

For about a decade, as I flew a lot, I met a lot of mid level executives at all sorts of companies. I routinely asked them to describe if their company used any derivative products, and which, and why. I was astounded to learn pretty much everyone did, from pricing plastics, to dealing with international trade variations, to getting financing for projects.

There is a reason the derivatives market has a notional value of ~1 quadrillion, and it's not because the people using them are all idiots. Quite the contrary, this value is there because it adds value across every sector of the world economy, and business the world over voluntarily use these products because they deem it in their best interests, which almost universally is because it lowers costs and/or volatility.

This [1] claimed 94% of the world's biggest companies used derivatives, and this was in 2009. I'd expect more and more of them to use derivatives over time as more products get priced.

All this followed from the ideas in Black-Scholes, for pricing certain contracts, ideas which were later developed to handle all sorts of products. Before this, people did a lot of the pricing mostly by guesswork, making it much harder to design and use all these volatility reducing products.

[1] https://derivsource.com/2009/04/23/over-94-of-the-worlds-lar...

[willdearden]

LTCM's blowup had nothing to do with any flaw in Black-Scholes. They did lose money on equity volatility strategies but it was because they were betting that volatility in the future would be lower than the volatility implied by Black-Scholes. Volatility ended up going up and they lost money. They lost money because their forecast of volatility was wrong, not because Black-Scholes was wrong about the market's view of volatility.

[jevgeni]

Financial crises are what financial model assumptions become when they grow up.

[brockwhittaker]

> One of those things that perhaps it would have been better that they had not invented.

I think you're off base on this. The ensuing financial mishaps just made the model better, but the creation of Black-Scholes brought us from 0% to 90% of the way to where we are today, where modern derivatives insure product price swings for almost everything across the world. Since then, a patch-work of model changes have brought us closer to perfect pricing through the realization that many markets have higher kurtosis.