The Black-Scholes formula, explained (2019)
cantorsparadise.com
The Black-Scholes formula, explained (2019)
1–10 of 66 posts
Re: The Black-Scholes formula, explained (2019)
#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 losses are in the tails, and the tails are no where near normal
Re: The Black-Scholes formula, explained (2019)
#3"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 initial assumptions, and—to a large degree—having been shown, empirically, to work.
(This is not your fault. Popular writing on the topic is terrible, elevating drama over accuracy. Against the Gods is one of the better ones, and doesn’t require much math.)
Re: The Black-Scholes formula, explained (2019)
#4"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…
How can an individual trader use the formula?
Re: The Black-Scholes formula, explained (2019)
#5"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.
Re: The Black-Scholes formula, explained (2019)
#6"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'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.
Re: The Black-Scholes formula, explained (2019)
#7"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.
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.
Re: The Black-Scholes formula, explained (2019)
#8"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'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
Re: The Black-Scholes formula, explained (2019)
#9"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 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.
Re: The Black-Scholes formula, explained (2019)
#10[flagged]