The Black-Scholes formula, explained (2019) • Hacker News Board

Re: The Black-Scholes formula, explained (2019)

#61

Post by worik » Mon, Apr 12, 2021, 7:33 AM UTC

jevgeni wrote: post #58

JumpCrisscross wrote: post #43

Earlier quoted context omitted.

> We never recalibrate the g constant in our calculations nor we wait a person to announce what the g for this quarter will be Sure. But we do update all manner of atmospheric, gravitometric and similar factors in our flight and orbital models. Once again, calibration frequency is a poor predictor of model quality. There are useless models in every domain involving immutable constants. And there are very good numeric…

Planes don't crash all at once every few years and resume flying only when the airports renegotiated the basic laws of physics. What you are referring to as "re-calibration" in planes and rockets is actually stochastic control and is a completely different topic to calibrating a stochastic model. But hey, I guess you like your metaphors like your risk models: incorrect. Wilmott covered model robustness and calibratio…

Some sense.

Comparing financial markets to physics is pretty much what made it all explode last two times.

It is getting ready to explode again.

The asset market has been sedately rising for a decade. Which makes models like really good.

\sarcasm{ON} This time is different \sarcasm{OFF}

No it is not.

Re: The Black-Scholes formula, explained (2019)

#62

Post by worik » Mon, Apr 12, 2021, 7:39 AM UTC

mbustamanter wrote: post #20

worik wrote: post #2

"Since its introduction in 1973 and refinement in the 1970s and 80s, the model has become the de-facto standard for estimating the price of stock options" ...and has caused a lot of catastrophic losses. The formula depends on a normal distribution and financial returns are random but not independent. They are not normal. The formula works, mostly, but when it does not it is worse than useless. Financial gains and los…

I remember that in a graduate class the professor told that among the important contributions of the theory was the BS formula. He never told us precisely what you wrote: P/L is in the tails. I wonder if he knew that LTCM went bust, while taking pride in being advised 'by two Nobel Prize recipients'.

Yes. The tails.

LTCM went bust because they thought they new better than the market and they were very very greedy. Very.

There is no formula for the market. The EMH in its weak form is correct. Has not been proved, but it is like P!=NP. True.

I am dismayed but unsurprised that financail models get so much support here.

You get money by working. Investments are savings. Just because there is some fool driving a Ferrari does not make that untrue, you cannot see the rest of the finance geeks flipping burgers.

Greed. Hubris. Bankruptcy.

Re: The Black-Scholes formula, explained (2019)

#63

Post by worik » Mon, Apr 12, 2021, 7:41 AM UTC

sprash wrote: post #5

worik wrote: post #2

"Since its introduction in 1973 and refinement in the 1970s and 80s, the model has become the de-facto standard for estimating the price of stock options" ...and has caused a lot of catastrophic losses. The formula depends on a normal distribution and financial returns are random but not independent. They are not normal. The formula works, mostly, but when it does not it is worse than useless. Financial gains and los…

The fact that the implied returns distribution is not normal is more or less "priced in". This is why you get volatility "smiles" and "skews". From the volatility surface (Volatility in respect to strike and time until settlement) you can easily calculate the propability density function for what the market assumes to be the future price. This is rarely if ever Gaussian, true, but it is not fundamentally wrong.

The financial returns are not normal.

It is not "priced in"

It goes up up up... crash.

Every generation has to learn this. I just hope we put the bankers in jail where they belong next time rather than bail them out.

Re: The Black-Scholes formula, explained (2019)

#64

Post by worik » Mon, Apr 12, 2021, 7:42 AM UTC

jevgeni wrote: post #60

kolbe wrote: post #30

Earlier quoted context omitted.

I don’t know why you’re getting downvoted. While what you said isn’t exactly correct, it’s pretty close. One reason for black scholes today is that it is a decent interpolation function. It is significantly easier to create an implied volatility function to interpolate with than it is to create a price function to interpolate with directly. Another is that regardless of the smile, the real delta of an option is prett…

I am being flippant about a topic where HN readership thinks that their cursory knowledge of it makes them experts. I mean, I agree with you. But to me, the whole complexity is just moved to vol modeling. BS with its economic assumptions is just an empty shell now, so to speak.

You are flippant.

I am deeply cynical

Re: The Black-Scholes formula, explained (2019)

#65

Post by ZephyrBlu » Mon, Apr 12, 2021, 7:46 AM UTC

JumpCrisscross wrote: post #37

ZephyrBlu wrote: post #35

Earlier quoted context omitted.

Interesting job! No creativity makes it sound like the market has been figured out. I know that isn't true, so does that mean that the risk/reward of strategies has flattened off (I.e. same risk for less reward) because there are less opportunities to exploit?

Thank you! It was. > No creativity makes it sound like the market has been figured out That was my bet. It has, so far, been a good one. > does that mean that the risk/reward of strategies has flattened off (I.e. same risk for less reward) because there are less opportunities to exploit? Your instinct was on point. You don’t need someone with a feel for volatility to make money (or not lose it) in options market maki…

Thanks for your perspective and no worries! It's always interesting to hear the opinions of people with domain expertise.

Re: The Black-Scholes formula, explained (2019)

#66

Post by FabHK » Mon, Apr 12, 2021, 9:46 AM UTC

xtracto wrote: post #53

jcfrei wrote: post #9

Earlier quoted context omitted.

I think the phrase "the de-facto standard for estimating the price of stock options" is just imprecise. It's the standard for generating the statistics like implied volatility, etc. But it's definitely not used to estimate the fair price of a new option, there are much newer models and methods to do that.

This. Back in 2006 when i was doing my PhD in CompSci + Options markets, the Binomial model was the state of the art. IIRC Black-Scholes was usef for historical references, and to understand the underlying variables given the simple assumptions "'closed world" it has. For example, the fact that it serves only for European options.

One should maybe distinguish the model (eg Black Scholes market (fixed vol), Dupire local vol, Heston stochastic vol, Merton jump diffusion, etc.) from the technique one uses to compute prices within the model (analytic closed form, PDE, tree (binomial or trinomial), Monte Carlo, other numeric methods).

All of the models (and techniques) I mentioned were well known and in use by 2000.