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Stuart_Armstrong comments on When the uncertainty about the model is higher than the uncertainty in the model - LessWrong
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Comments (78)
Ok, here's an obvious failure: volatility smiles. Except that that's known and you can't exploit it. And people tend to stop using BS for predicting large market swings. Most of the opportunities for exploiting the flaws of BS are already covered by people who use BS+patches. There might be some potential for long term investments, though, where investors are provably less likely to exploit weaknesses.
Even if there's a known failure, though, you still might be unable to exploit it. In some situations, irrational noise traders can make MORE expected income that more rational traders; this happens because they take on more risk than they realise. So go broke more often, but, still, an increasing fraction of the market's money ends up in noise traders' hands.
Why is it a failure and a failure of what, precisely?
Sense make not. Black-Scholes is a formula describing a relationship between several financial variables, most importantly volatility and price, based on certain assumptions. You don't use it to predict anything.
I don't quite understand that sentence as applied to reality. The NBER paper presents a model which it then explores, but it fails to show any connection to real life. As a broad tendency (with lots of exceptions), taking on more risk gives you higher expected return. How is this related to Black-Scholes, market failures, and inability to exploit market mispricings?
Come on now, be serious. Would you ever write this:
"General relativity is a formula describing a relationship between several physical variables, most importantly momentum and energy, based on certain assumptions. You don't use it to predict anything." ?
I am serious. The market tells you the market's forecast for the future via prices. You can use Black-Scholes to translate the prices which the market gives you into implied volatilities. But that's not a "prediction" -- you just looked at the market and translated into different units.
Can you give me an example of how Black-Scholes predicts something?
BS is not just an equation, it is also a model. It predicts the relationships between the volatility and price of the underlying assets, and price of the derivative (and risk free rate, and a few other components). In as much as you can estimate the volatility (the rest is pretty clear) you can see whether the model is correct. And it often is, but not always:
See for instance: http://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Black.E2.80.93Scholes_in_practice
Now you might say that the equation shouldn't be used as a model... but it is, and as such, makes predictions.
Yes. Or, rather, there is a Black-Scholes options pricing model which gives rise to the Black-Scholes equation.
No, it does not predict, it specifies this relationship.
Heh. And how are you going to disambiguate between your volatility estimate being wrong and the model being wrong?
Let me repeat again: Black-Scholes does not price options in the real world in the sense that it does not tell you what the option price should be. Black-Scholes is two things.
First, it's a model (a map in local terms) which describes a particular simple world. In the Black-Scholes world, for example, prices are continuous. As usual, this model resembles the real world in certain aspects and does not match it on other aspects. Within the Black-Scholes world, the Black-Scholes option price holds by arbitrage -- that is, if someone offers a market in options at non-BS prices you would be able to make riskless profits off them. However the real world is not the Black-Scholes world.
Second, it's a converter between price and implied volatility. In the options markets it's common to treat these two terms interchangeably in the recognition that given all other inputs (which are observable and so known) the Black-Scholes formula gives you a specific price for each volatility input and vice versa, gives you a specific implied volatility for each price input.
And specifies it incorrectly (in as much as it purports to model reality). The volatility smile is sufficient to show this, as the implied volatility for the same underlying asset is different for different options based on it.
Yes, there's a reason we look at options-implied vol - it's because B-S and the like are where we get our estimates of vol from!
In the sense that Black-Scholes converts prices to implied volatility, yes. However implied volatility from the options markets is a biased predictor of future realized volatility -- it tends to overestimate it quite a bit.