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The Black-Scholes/Merton equation [video]

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Re: The Black-Scholes/Merton equation [video]

#81

Post by JumpCrisscross »

mhh__ wrote: post #24
JumpCrisscross wrote: post #3

Earlier quoted context omitted.

Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity

Taleb and Derman have argued that put call parity implies BS but other disagree quite strongly.

> Taleb and Derman have argued that put call parity implies BS but other disagree quite strongly

I mean sure. They're related. Same way the Michelson-Morley experiment implied special relativity. That doesn't detract from Einstein specifying just how. (Derman is legit but Taleb is a hack.)

Re: The Black-Scholes/Merton equation [video]

#83

Post by helsinkiandrew »

lupire wrote: post #31
dr1ver wrote: post #23

Earlier quoted context omitted.

Volatility is a bit more predictable than price. And there are more complex formulae that also model volatility rather than treat it as a constant.

If volatility is predictable, it would quickly be traded until it became unpredictable and unprofitable.

People have been trading options and futures on the volatility of the S&P500 for years:

https://www.cboe.com/tradable_products/vix/vix_options/

Re: The Black-Scholes/Merton equation [video]

#84

Post by seanhunter »

RichardCA wrote: post #59
RandomLensman wrote: post #56

Earlier quoted context omitted.

How would you connect the two events?

I don't know what the mathematical underpinnings of those mortgage-backed derivatives were, but I know someone somewhere looked at all that math and decided the risk burden was acceptable. No one said hey, wait, the model is only as good as the assumptions you feed into it. The movie The Big Short got at this, but it was just a movie with Steve Carell standing in for that shocked person who doesn't seem to have reall…

LTCM wasn't caused by anything like mortgage-backed securites.

LTCM was doing ultra-leveraged short-term trades of various kinds. When they started these were arbitrages of various kinds so they had low risk and a solid edge but as more capital flowed into their fund, the capacity of those trades was exhausted and they put money into riskier other trades. Some of their counterparties were big banks who parked overnight funds in LTCM and then when they got spooked by some losses and yanked those funds, LTCM lost a staggering amount of money very quickly as a result and went bust. If you want an excellent book about LTCM, "When Genius Failed" is one of the best books ever written about the history of financial markets.

The origins of the subprime mortgage crisis were a lot more complicated than most people give credit for and in particular I really wouldn't take "the big short" as any kind of reliable guide. For a good critical view of the crisis written by someone who actually knows what they are talking about I would recommend "Fools Gold" by Gillian Tett.

Financial crises and crashes have happened since the dawn of human history and will probably continue to happen. Suffice to say that the 2008 crisis had nothing to do with thing things that caused LTCM to fail, and neither of them have anything to do with the insight behind the Black/Scholes/Merton model other than the fact that Scholes and Merton were I think on the board of LTCM.[1]

[1] Fun fact, the other one of the three, Fischer Black was a quant at Goldman Sachs. So there's your 2008 crisis connection[2]

[2] Or not. Fischer Black died in 1995.

Re: The Black-Scholes/Merton equation [video]

#85

Post by throwawayFinX »

helsinkiandrew wrote: post #83
lupire wrote: post #31

Earlier quoted context omitted.

If volatility is predictable, it would quickly be traded until it became unpredictable and unprofitable.

People have been trading options and futures on the volatility of the S&P500 for years: https://www.cboe.com/tradable_products/vix/vix_options/

This is also (slightly) incorrect.

When trading the VIX, you are trading the implied volatility not the actual (realized) volatility.

VIX represents the implied vol of options on S&P500 expiring 30 days into the future.

Trading the realized volatility is not easy :)

Re: The Black-Scholes/Merton equation [video]

#86

Post by vikramkr »

exclipy wrote: post #44
vikramkr wrote: post #38

Earlier quoted context omitted.

Yep. You can make money off of using options as a way of betting on what the volatility measure itself will be. If you think the historical standard deviation is lower than what it will be because of some new change to the company or the world environment, and your view is different from the market's view. It's why sometimes very out of the money call options will paradoxically go up in price after really bad news -…

Is that a bug in the equation that one could take advantage of?

Not really. The equation is just saying "based off these assumptions here is the best price" and you would make money if your assumptions differ from market assumptions in a favorable direction. Arbitrage is the closest to exploiting "bugs" in finance to get risk free returns but in a liquid enough market all these obvious opportunities quickly close (if there's free money on the ground, someone will pick it up, and then there's no more free money ond the ground. Some hedge funds build ultra fast private internet networks just to be able to pick up that free money nanoseconds faster than someone else). It's more that the equation is telling you if you think you have a better estimate for some of these values, what you should be willing to pay.

Re: The Black-Scholes/Merton equation [video]

#87

Post by sgjohnson »

runarberg wrote: post #21
sgjohnson wrote: post #16

Earlier quoted context omitted.

Derivatives are a zero-sum game. If someone lost a trillion dollars trading them, someone else made a trillion dollars trading them. It will always result in a net 0.

I agree that they are a zero sum game, but I’d argue that the sum is a net positive for traders over a long period of time, and the people who are systematically loosing are the workers who’s true earnings were siphoned away from them and onto the stock market, where they are sold as derivatives. This manifests in e.g. how much cheaper it is for people to borrow money who hold a large stock portofolio, how interests…

What workers are you even talking about?

Re: The Black-Scholes/Merton equation [video]

#88

Post by KMag »

JumpCrisscross wrote: post #80
dist-epoch wrote: post #26

Earlier quoted context omitted.

This equation is an idealized option, a spherical cow. If one would actually use it to price options one would lose money. There are many empirical option pricing features that this equation can't explain - the "smile", the "skew", ...

> If one would actually use it to price options one would lose money If you try to fly a rocket across the solar system using only Newton's equations, it will crash. That doesn't make Newtonian mechanics useless. Almost every option-pricing engine in the market starts with Black-Scholes-Merton. Smiles and skews are all dealt with on the vol surface--it's an expandable variable.

One thing that seems not widely understood is that the assumption of normal or log-normal distributions in stochastic calculus is like the assumption of linearity in most engineering fields. It's known to be incorrect, but you can do a heck of a lot with piecewise-linear model. Similarly, using a normal or log-normal assumption within a range of parameters (such as the volatility smile) is really useful.

Part of the reason a Gaussian distribution is used so much is that you need a stable distribution if you want to be able to perform algebra on your random variables. The variance of the Cauchy distribution is undefined and the variance of the Levy distribution is infinite, so Gaussian is really the go-to distribution.

Re: The Black-Scholes/Merton equation [video]

#89

Post by runarberg »

sgjohnson wrote: post #87
runarberg wrote: post #21

Earlier quoted context omitted.

I agree that they are a zero sum game, but I’d argue that the sum is a net positive for traders over a long period of time, and the people who are systematically loosing are the workers who’s true earnings were siphoned away from them and onto the stock market, where they are sold as derivatives. This manifests in e.g. how much cheaper it is for people to borrow money who hold a large stock portofolio, how interests…

What workers are you even talking about?

The workers of the companies who’s derivatives are being traded on the stock market.

But also just workers in general. The amount of people who can not just make a living, but make them selves millionaires on the stock market is held up by the fact that workers in general are not getting the profits they generate. These profits are being siphoned to Wall Street, and used to pay for the lavish lifestyles of Wall Street traders who get to use the profits generated by the workers.

Re: The Black-Scholes/Merton equation [video]

#90

Post by lamontcg »

cubefox wrote: post #51
eternauta3k wrote: post #17

Earlier quoted context omitted.

Are you talking about backpropagation in neural networks? Do you mean as a differential equation? It already is a normal algebraic equation.

Yes in neural networks. Backpropagation is probably worth more than the equation in the video. But it's an algorithm, which aren't usually expressed as equations.

Backpropagation is just the chain rule from basic calc. Done on a massive scale in something like an LLM. You can absolutely express it as equations.
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