...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
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.)
>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.
But nobody prices options while assuming all the good old innocent assumptions underlying the original derivation of the formula. That, indeed, can be seen from the fact that different vols will be quoted for different strikes at the same expiry.
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.
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.
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.
Their fault for violating GDPR by trying to put cookies without my permission! Ha!
Edit: docked for bad sense of humor (mine or of downvoters - of that I am not sure)
Thoughts:
- Since you have a right but not an obligation to buy/sell, that creates asymmetry. Since it's asymmetric, a wider range of outcomes, ie higher vol (imagine your gaussian curve on top of the hockey stick), makes the option worth more.
- Similarly having more time to expiry makes the option worth more, the range of outcomes is more spread out.
- There's a whole bunch of Greeks that the books will go through, but the intuition is the same for all of them. You can work out what's good or bad for you from thinking about how the distribution of outcomes is affected by a change in whatever.
- To trade the vol and not a mix of the vol and the direction, you flatten your delta by trading the underlying. If you do this at some point on the option price vs underlying price curve, you can get the graph to be flat, ie neutral to small price moves. But you can't make it flat everywhere with a hedge, because of course the graph is bendy.
- Near the strike where the bend is in the hockey stick is where it curves the most. On one extreme the option is worthless, on the other it's the same as having the underlying.
- As time passes it's got to get more curvey at the strike, less curvey on the sides.
- Curveyness on the price graph is called gamma. This is the gamma that ended up biting with the GME squeeze, by the sound of it. The problem is if you are short options, the graph looks like an upside down parabola, so if the underlying moves up a lot you will be short and getting shorter. If it moves down a lot, you'll be getting longer and longer. This is bad.
- It doesn't actually matter whether you are buying the right to buy or the right to sell. If you're buying, you have a positive gamma. But how? Well since owning a put and shorting a call of the same strike (or vice versa) should give you no curvature (looks like a straight line) they must have the same curvature. In the business people just call options with higher strikes than the current underlying price "calls" and options with lower strikes "puts" regardless of what they actually are. In-the-moneys just have some more premium attached to them, but act the same (in terms of everything other than delta) as their partner out-of-the-money option at that strike.
- Why do people get short gamma, knowing that movement is bad for them? Of course the option costs something to the guy who buys them. As long as the movement isn't too much it might be worthwhile to be short. In fact, most of the time the movement isn't enough to justify the price.
These two observations become unified when one observes that the two variables sigma (vol) and (T-t) (time to expiry) only ever enter the Black-Scholes formula together, as sigma^2 (T-t) (which is the variance of the log return to expiry).
(That leads to the observation that the unit of vol is 1/sqrt(time), normally a^(-1/2) [a=annum=year]).
Next, you alluded to it, but let's make explicit the way to trade implied vol: Suppose (WLOG) that you think implied vol is too low. Then you buy it (buy cheap, sell expensive...) in the market (buy buying calls and/or puts). Now you're long gamma, but short theta, and long vol in two senses: a) if the stock doesn't move, but implied vol goes up, you can turn around and sell the option back for a profit. b) you can delta hedge the option. Every day, you lose money on theta, but gain money on the movements of the stock. If it doesn't move at all, you lose the theta. If the stock moves "as expected" (=as implied by the implied vol), you'll just break even. But if the stock moves more than expected (that is, realised vol is higher than the implied you bought it at), then you make money. If the market comes around to your estimate of the future vol, you can then sell the option at a profit, or you can hold it to the end and keep delta hedging, and that will be profitable if realised vol turns out to be higher than implied.
If the market is too high on volatility: sell the option and you'll end up paying less in delta-hedging costs.
If that market is too low on volatility: do the opposite.
> 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
The only contemporary use for BS by professionals is as a convention for quoting volatility. As a pricing model it does not account for key effects such as the permanent "volatility smile" appearing in the aftermath of the 1987 crash (significantly increased price of downside options), and well understood behaviours like jumps and volatility clustering.
