6 ms·

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 volatili

by sprash 6y ago

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.

jevgeni 6y ago
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.
- sprash 6y ago
  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.
  - jevgeni 6y ago
    “Expensive” (at least for market makers) means you have to maintain a staff of quants whose job is to essentially create a curtain of rigor and hide the fact that traders usually rely on a bunch of simpler models to judge the broad dynamics and their gut for actual business decisions.
- kolbe 6y ago
  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 pretty damn close to black-scholes delta. So, you can maintain prices in real time as a function of the underlying price pretty accurately. A third (and this is important) is that trading systems have it built in as a way to interface with them. People know black-scholes and it isn’t proprietary. So you can do all sorts of research on the dynamics of a volatility smile, and it can be orthoganol to someone doing research on expected dividends or what the actual value of the underlying is. And you can bring all those pieces back together via the black scholes equation. A fourth reason tied into machine learning: implied volatilities behave just much better than raw interpolated prices when running them through predictive algorithms.
  - jevgeni 6y ago
    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.
    - worik 6y ago
      You are flippant. I am deeply cynical
worik 6y ago
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.

by sprash 6y ago

jevgeni 6y ago

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.

sprash 6y ago
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.
- jevgeni 6y ago
  “Expensive” (at least for market makers) means you have to maintain a staff of quants whose job is to essentially create a curtain of rigor and hide the fact that traders usually rely on a bunch of simpler models to judge the broad dynamics and their gut for actual business decisions.
kolbe 6y ago
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 pretty damn close to black-scholes delta. So, you can maintain prices in real time as a function of the underlying price pretty accurately. A third (and this is important) is that trading systems have it built in as a way to interface with them. People know black-scholes and it isn’t proprietary. So you can do all sorts of research on the dynamics of a volatility smile, and it can be orthoganol to someone doing research on expected dividends or what the actual value of the underlying is. And you can bring all those pieces back together via the black scholes equation. A fourth reason tied into machine learning: implied volatilities behave just much better than raw interpolated prices when running them through predictive algorithms.
- jevgeni 6y ago
  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.
  - worik 6y ago
    You are flippant. I am deeply cynical

worik 6y ago

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.