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The Black-Scholes formula, explained (2019)

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

#51

Post by FabHK »

spekcular wrote: post #6
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'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 .

Well, everybody uses standard B-S to quote option prices, just like everyone uses interest rates to quote bond prices.

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.

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

#52

Post by tedunangst »

stainforth wrote: post #46
JumpCrisscross wrote: post #39

Earlier quoted context omitted.

> lot of "no bid" on many OTM strikes. So it looks like the market makers were simply stepping away Bingo. Self help [1] and circuit breakers [2] negate the unsolvable edge case: large, instantaneous price movements. [1] https://www.reuters.com/article/usa-options-cboe-idUSL2N1H40... [2] https://www.npr.org/2020/03/09/813682567/how-stock-market-ci...

All that promise that innovation like HFT among other things was fine because of the value liquidity they can provide and now they can just choose to not play if they don't want to.

Near the money GME options are super liquid with tight spreads, exactly as promised. If you're holding GME, but you're worried about an earning surprise, you can put on a collar for like zero cost, which is pretty crazy considering the insane volatility. Exactly what the people who said they wanted the markets to support meaningful transactions instead of speculation asked for. Nobody ever promised you'd get easy access to 1000:1 yolo lottery tickets.

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

#53

Post by xtracto »

jcfrei wrote: post #9
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 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.

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

#54

Post by JumpCrisscross »

jzwinck wrote: post #48
JumpCrisscross wrote: post #27

Earlier quoted context omitted.

> the inputs of the BS model are forecasts In the same way a rocket flight model is forecasting the arrangement of air molecules it’s about to run into. They’re instantaneous forecasts that are dynamically updated. No long-term forecasting involved. At the end of the day, options market makers haven’t blown up since the early noughties. (LTCM got sunk by non-options bets.) They are low-margin, low-risk businesses. It…

If options pricing is largely solved, do you think exchanges could provide an API where instead of specifying the price and quantity for hundreds or thousands of options on a stock, market makers could send a much smaller message containing their latest risk and model parameters, and have the exchange run a standard model internally to generate the quotes? Since the model to convert parameters to prices and quantitie…

> market makers could send a much smaller message containing their latest risk and model parameters, and have the exchange run a standard model internally to generate the quotes?

No market works like this. The smaller-still message of a price is sent and disseminated. When you buy a flight, you want the price of the ticket—not the airline’s fuel and tariff costs.

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

#55

Post by whatever1 »

FabHK wrote: post #49
whatever1 wrote: post #26

Earlier quoted context omitted.

All of the inputs of the BS model are forecasts. All of them can be wrong, and they have been wrong countless times. It’s like saying that your linear extrapolation for the stock market mostly works, except for the times it doesn’t.

None of the inputs to the BS model are forecasts, except the volatility. What the BS model allows, then, is trading this volatility. (Just as other financial products require other inputs, and thus make them, in a sense, tradable: Cross currency swaps make the cross currency basis tradable, credit default swaps make credit risk tradable, trading index vol versus single stock vol makes correlation tradable, etc.)

The only thing it offers, is a common denominator for trading. The value predicted by the model itself is completely arbitrary. You have no clue today about tomorrows volatility or the the interest of a “risk free” instrument aka the central banker can show up tomorrow announcing -10% interest rates.

Btw when interest rates went negative for the first time, many trading shops were caught pants down, because of course their models did not have a provision for negative interest rates.

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

#56

Post by freebee56 »

I used to work on options MM desk. Even though BS is not correct in magnitude (e.g. our quants used some black magic to get deltas at the tails, which even then we're quite off from what CME was giving) it is directionally correct. Just having an intellectual grasp of what caused a shift in the price can be very useful. The problem IMHO is that way too much energy has been spent improving it by old school quants vs exploring other approaches ( e.g. a limes regression works quite well for daily fx option movements)

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

#58

Post by jevgeni »

JumpCrisscross wrote: post #43
whatever1 wrote: post #42

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.

> 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 calibration frequency. Any time you have to adjust an unobserved term in your SDE (like market price of risk, for example) you are changing the model. So if your model has to be changed every x minutes else it gives wrong results, you're not "adjusting your inputs", you are just using T/x shitty models.

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

#59

Post by jevgeni »

FabHK wrote: post #50
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.

One should clarify that basically nobody tries to "predict" anything with Black Scholes, just as basically nobody "predicts" share prices by doing a discounted cash flow analysis. Yet, they each provide the conceptual framework for trading (of options and stocks, respectively) in such a way that those that have better predictive power make money, on average, at the expense of those traders that don't. With that, they…

It's a market convention, with as much predictive power as knowing options used to be quoted in vol points.

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

#60

Post by jevgeni »

kolbe wrote: post #30
jevgeni wrote: post #7

Earlier quoted context omitted.

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.

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.

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