So why don’t you become rich by exploiting this failure? If Black-Scholes fails in an obvious (to you) manner, options in the market must be mispriced and you can make a lot of money from this mispricing.
In this case you don’t have to wait for the market to become rational. If the options are mispriced, you will be able to realize your (statistically expected) gains at the expiration.
Financial instruments that expire (like options or, say, most bonds) allow you to take advantage of the market mispricing even if the market continues to misprice the securities.
True, but if most of your statistically expected gains comes from rare events, you can still go broke before you get a winning lottery ticket, even if the lottery is positive expected value. I have no idea if there are any real-world financial instruments that work like this, though.
if most of your statistically expected gains comes from rare events, you can still go broke before you get a winning lottery ticket, even if the lottery is positive expected value.
True—that’s why risk management is a useful thing :-)
And yes, options are real-world financial instruments that work like that.
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?
people tend to stop using BS for predicting large market swings
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.
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.
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:
Yes. Or, rather, there is a Black-Scholes options pricing model which gives rise to the Black-Scholes equation.
It predicts the relationships
No, it does not predict, it specifies this relationship.
In as much as you can estimate the volatility (the rest is pretty clear) you can see whether the model is correct.
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.
No, it does not predict, it specifies this relationship.
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.
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.
Just because you can pick a strategy that should have an expected postivie return doesn’t mean that you automatically get rich. People do drown in a river of average depth of 1 meter.
Knowing that there is a mispricing doesn’t tell you what the correct price actually is, which is what you need to know in order to make better money than random-walk models.
Knowing that there is a mispricing doesn’t tell you what the correct price actually is
In this particular case the problem mentioned is too thin tails of the underlying distribution. If you believe the problem is real, you know the sign of the mispricing and that’s all you need.
For this particular example, this basically means that you can predict that LTCM will fail spectacularly when rare negative events happen. But could you reliably make money knowing that LTCM will fail eventually? If you buy their options that pay off when terrible things happen, you’re trusting that they’ll be able to pay the debts you’re betting they can’t pay. If you short them, you’re betting that the failure happens before you run out of money.
But could you reliably make money knowing that LTCM will fail eventually?
Just LTCM, no. But (if we ignore the transaction costs which make this idea not quite practicable) there are enough far-out-of-the-money options being traded for me to construct a well-diversified portfolio that would allow me to reliably make money—of course, only if these options were Black-Scholes priced on the basis of the same implied volatility as the near-the-money options and in reality they are not.
IIRC, LCTM ended up in disaster not only because of a Russian default/devaluation. They had contracts with Russian banks that would have protected them, except that the Russian government also passed a law making it illegal for Russian banks to pay out on those contracts. It’s hard to hedge against all the damage a government can do if it wants.
As a historical note, the LTCM crisis was caused by Russias default, but LTCM did not bet on Russia or rely on Russian banks. LTCMs big bet was on a narrowing of the price difference between 30 year treasurys and 29 year treasurys. When Russia defaulted people moved out of risky assets into safe assets and lots of people bought 30 years. That temporary huge burst in demand led to a rise in the price of 30s. Given the high leverage of LTCM that was enouph to make them go bust.
This is correct. LTCM’s big trade was a convergence trade which was set up to guarantee profit at maturity. Unfortunately for them LTCM miscalculated volatility and blew up because, basically, it could not meet a margin call.
BS fails even on purely financial issues—its tails are just too thin.
So why don’t you become rich by exploiting this failure? If Black-Scholes fails in an obvious (to you) manner, options in the market must be mispriced and you can make a lot of money from this mispricing.
The market can stay irrational longer than you can stay solvent.
In this case you don’t have to wait for the market to become rational. If the options are mispriced, you will be able to realize your (statistically expected) gains at the expiration.
Financial instruments that expire (like options or, say, most bonds) allow you to take advantage of the market mispricing even if the market continues to misprice the securities.
True, but if most of your statistically expected gains comes from rare events, you can still go broke before you get a winning lottery ticket, even if the lottery is positive expected value. I have no idea if there are any real-world financial instruments that work like this, though.
True—that’s why risk management is a useful thing :-)
And yes, options are real-world financial instruments that work like that.
The assumption here is that the options are being priced with Black-Scholes, which I don’t think is true.
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.
Just because you can pick a strategy that should have an expected postivie return doesn’t mean that you automatically get rich. People do drown in a river of average depth of 1 meter.
Knowing that there is a mispricing doesn’t tell you what the correct price actually is, which is what you need to know in order to make better money than random-walk models.
In this particular case the problem mentioned is too thin tails of the underlying distribution. If you believe the problem is real, you know the sign of the mispricing and that’s all you need.
For this particular example, this basically means that you can predict that LTCM will fail spectacularly when rare negative events happen. But could you reliably make money knowing that LTCM will fail eventually? If you buy their options that pay off when terrible things happen, you’re trusting that they’ll be able to pay the debts you’re betting they can’t pay. If you short them, you’re betting that the failure happens before you run out of money.
Just LTCM, no. But (if we ignore the transaction costs which make this idea not quite practicable) there are enough far-out-of-the-money options being traded for me to construct a well-diversified portfolio that would allow me to reliably make money—of course, only if these options were Black-Scholes priced on the basis of the same implied volatility as the near-the-money options and in reality they are not.
This assumes the different black swans are uncorrelated.
Yes, to a degree. However in this particular case I can get exposure to both negative shocks AND positive shocks—and those certainly are uncorrelated.
LTCM should not be your counter-party! Also, using a clearinghouse eliminates much of the risk.
IIRC, LCTM ended up in disaster not only because of a Russian default/devaluation. They had contracts with Russian banks that would have protected them, except that the Russian government also passed a law making it illegal for Russian banks to pay out on those contracts. It’s hard to hedge against all the damage a government can do if it wants.
As a historical note, the LTCM crisis was caused by Russias default, but LTCM did not bet on Russia or rely on Russian banks. LTCMs big bet was on a narrowing of the price difference between 30 year treasurys and 29 year treasurys. When Russia defaulted people moved out of risky assets into safe assets and lots of people bought 30 years. That temporary huge burst in demand led to a rise in the price of 30s. Given the high leverage of LTCM that was enouph to make them go bust.
Thanks for the correction—I had once seen part of a documentary on LCTM and that was what I remembered from it.
This is correct. LTCM’s big trade was a convergence trade which was set up to guarantee profit at maturity. Unfortunately for them LTCM miscalculated volatility and blew up because, basically, it could not meet a margin call.