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

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

#11

Post by jevgeni » Sun, Apr 11, 2021, 9:27 PM UTC

JumpCrisscross wrote: post #3

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…

> formula depends on a normal distribution and financial returns are random but not independent...worse than useless. This is sort of like throwing out physics because Newtonian mechanics don’t account for fluid dynamics. Yes, the original theory assumed that away. And yes, the original theory is taught in undergrad. But the work has been developed far past its original, adjusting for or incorporating away those init…

Having two sets of assumptions for buy and sell side is pretty indicative of the quality of the model.

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

#12

Post by mikkom » Sun, Apr 11, 2021, 9:29 PM UTC

Oh how I hate these Medium posts that are not readable without doing something (registering/installing app/paying.. whatever)

I feel like Medium is the new expertsexchange. I remember how much I hated the site always when I ended there and I seem to have very similar feelings towards Medium.

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

#13

Post by ivalm » Sun, Apr 11, 2021, 9:32 PM UTC

vardaro wrote: post #8

spekcular wrote: post #6

Earlier quoted context omitted.

I'm not in finance, but my impression from reading literature from those who are is that no one uses vanilla B–S for pricing options. One reason is the volatility smile: https://en.wikipedia.org/wiki/Volatility_smile .

The vol smile is mostly a byproduct of greater demand for far OTM options to hedge tail risk, alongside more sellers for ATM options which depresses the middle portion of the curve. I am not sure why this is a problem

It's an example of how real life pricing deviates from Black-Scholes. At the same time the pricing is correct in a sense that tail risks are greater than would be expected from a random walk.

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

#14

Post by silentsea90 » Sun, Apr 11, 2021, 9:35 PM UTC

mikkom wrote: post #12

Oh how I hate these Medium posts that are not readable without doing something (registering/installing app/paying.. whatever) I feel like Medium is the new expertsexchange. I remember how much I hated the site always when I ended there and I seem to have very similar feelings towards Medium.

Paywalling gender change information seems weird indeed.

Edit: docked for bad sense of humor (mine or of downvoters - of that I am not sure)

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

#15

Post by sprash » Sun, Apr 11, 2021, 9:36 PM UTC

jevgeni wrote: post #7

sprash wrote: post #5

Earlier quoted context omitted.

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.

That makes BS essentially a very expensive interpolation method, where you get to pretend to the auditors that you can hedge away your delta perfectly.

This only means that the real probability density function is parameterized by a sum of many Gaussian functions. Considering that the real implied returns are a skewed "gaussian-like thing" this is not the worst thing to do. Truly, using BS in this context is more or less historically motivated but I doubt there are far less "expensive" ways out there to find a suitable parameterization, what ever "expensive" means.

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

#16

Post by JumpCrisscross » Sun, Apr 11, 2021, 9:36 PM UTC

jevgeni wrote: post #11

JumpCrisscross wrote: post #3

Earlier quoted context omitted.

> formula depends on a normal distribution and financial returns are random but not independent...worse than useless. This is sort of like throwing out physics because Newtonian mechanics don’t account for fluid dynamics. Yes, the original theory assumed that away. And yes, the original theory is taught in undergrad. But the work has been developed far past its original, adjusting for or incorporating away those init…

Having two sets of assumptions for buy and sell side is pretty indicative of the quality of the model.

> two set of assumptions for buy and sell side is pretty indicative of the quality of the model

What does this refer to? And, no. Disagreement on inputs doesn’t convey much about a model—it’s a negotiation. Any model will have procurer and vendor using different inputs when negotiating purchase and sale. That Boeing and steel mill don’t agree on tensile strength assumptions doesn’t mean aircraft designers are winging it.

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

#17

Post by fegu » Sun, Apr 11, 2021, 9:42 PM UTC

silentsea90 wrote: post #14

mikkom wrote: post #12

Oh how I hate these Medium posts that are not readable without doing something (registering/installing app/paying.. whatever) I feel like Medium is the new expertsexchange. I remember how much I hated the site always when I ended there and I seem to have very similar feelings towards Medium.

Paywalling gender change information seems weird indeed. Edit: docked for bad sense of humor (mine or of downvoters - of that I am not sure)

Don't feel bad, at least I chuckled :)

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

#18

Post by mbustamanter » Sun, Apr 11, 2021, 9:45 PM UTC

JumpCrisscross wrote: post #3

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…

> formula depends on a normal distribution and financial returns are random but not independent...worse than useless. This is sort of like throwing out physics because Newtonian mechanics don’t account for fluid dynamics. Yes, the original theory assumed that away. And yes, the original theory is taught in undergrad. But the work has been developed far past its original, adjusting for or incorporating away those init…

>This is sort of like throwing out physics because Newtonian mechanics don’t account for fluid dynamics.

>having been shown, empirically, to work.

What exactly do you mean by this? That they are correct most of the time? Or that the person that uses them won't go bust?

This parallel between physical theories and assumptions about how the market works is bogus. In trading you can have strategies that are correct most of the time yet when they fail the impact of the loss can take you out.

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

#19

Post by jevgeni » Sun, Apr 11, 2021, 9:47 PM UTC

JumpCrisscross wrote: post #16

jevgeni wrote: post #11

Earlier quoted context omitted.

Having two sets of assumptions for buy and sell side is pretty indicative of the quality of the model.

> two set of assumptions for buy and sell side is pretty indicative of the quality of the model What does this refer to? And, no. Disagreement on inputs doesn’t convey much about a model—it’s a negotiation. Any model will have procurer and vendor using different inputs when negotiating purchase and sale. That Boeing and steel mill don’t agree on tensile strength assumptions doesn’t mean aircraft designers are winging…

Buy-side firms don’t use BS with the same assumptions as market makers. If you’re a fund manager, you are interested in objective estimates of the value. If you’re a market maker you want to show that you can perfectly replicate and thusly hedge your derivatives. Never mind that you have to recalibrate your model every 20 minutes.

For a model that is supposed to measure the objective value of an asset, that’s clear failure. BS is at this point just a vague market consensus which stinks more and more, the farther you stray away from vanilla European options.

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

#20

Post by mbustamanter » Sun, Apr 11, 2021, 9:50 PM UTC

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'.