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I am doing some reading on the (historical) emergence of the Black-Scholes implied volatility smile for index options (yes - post 87), and I stumbled across an economic paper attempting to explain the smile using ideas like update of rational expectations and state-dependent utility of representative investors...Unfortunately this was not the only paper I read, that sounded like that.

Aside from the volatility smile, this exercise made me think of fat tails in general, correlation of volatility, bubbles, crashes, etc. - and left me wondering if classical economics can explain any of them?

I have read a couple of explanations for economic rational bubbles, although the comparison of this theory, to empirical findings, appears to suggest it is inaccurate.

I am beginning to think classical economics is like religion: only useful if you actually believe in it. Are there any references that present a different view?

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    $\begingroup$ Don't know much about classical economics, but I'm guessing herding behavior is not included? ;) $\endgroup$ – H. Arponen Dec 12 '14 at 11:19
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    $\begingroup$ Read Nicholas Taleb. His answer is a clear no. $\endgroup$ – Deniz Dec 12 '14 at 19:12
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    $\begingroup$ No problem. :-) $\endgroup$ – Rusan Kax Dec 16 '14 at 19:26
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I would argue that indeed none of the so-called stylized facts you mentioned can be explained by classical economic theory.

That there was a gross delta between the predictions of classical economic theory and empirical data was foremost found out by Benoit Mandelbrot as far back as 1963 in his seminal paper:

The Variation of Certain Speculative Prices

In that papers he argues that there are no easy remedies for the shortcomings of classical economic theory so that you have start from scratch - this is what he did.

As an aside: I was fortunate enough to meet Benoit in person and have to say that he was a very impressive man - intellectually as well as personally.

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I think there is a slight misconception into the purpose of an economic theory. The market is a complex entity to be modeled and yes, it is neither efficient nor arbitrage free but it is trading and there is a price process that corresponds to the market one. You could say that classical economic theory has failed, but I would argue the idea of a theory is not to pretend to know everything but to posit a possible structure and then see if it is relevant in future results, making it a valid theory or an invalid one.

In fact, one could argue that merely observing empirical facts about the market (such as the skew,) do not mean anything really. Yes, you could use N-dimensional b-splines to model the volatility surface but tomorrow that surface might disappear and become constant. The idea is to be able to understand when and why it might become constant. Economic theory would try to explain that. It might not work well, but the idea is to come up with something that can construct a good understanding of the market. That seems to me, the purpose of the theory.

The argument lies in whether it is the best approach to this, and in fact, it has had some significant achievements in that regard, no arbitrage and efficiency being a few. If you can think of a better approach, by all means, a Nobel awaits.

Also, other economic models such as DSGE's might not work well, but it is well known that the FED and other central banks use them extensively. So they inevitably have an impact on the market, making them somewhat valid.

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  • $\begingroup$ Thank you for your answer - which is thoughtful and useful. Yes, models are not reality - and you raise an excellent point - but gloss over the important concept of -"falsification". From a scientific/empirical content point of view, a theory or model must first meet the falsifiable criterion - otherwise the theory is worth nil. Indeed, that is (one) of the problems with the DSGE models (which until 2008 did not even contain financial markets, not money). Your implication that extensive use imparts some degree of validity is...not something I would agree with. $\endgroup$ – Rusan Kax Dec 15 '14 at 16:18
  • $\begingroup$ Thats not what I said. I said, the idea is to build something that explains and helps to understand better. Its not a comment on a DSGE models usefulness, except in predicting Fed actions. So, there is a different use and a different validity then as an in probability explanation of the market. $\endgroup$ – Drew Dec 15 '14 at 17:00
  • $\begingroup$ OK. Sorry you seemed to be saying a number of different things. You suggest in your first line that I have a misconception of the purpose of economic theory. [Q: so what is the purpose of economic theory?]. In the following sentence you suggest you would argue economics has not failed - and argue that {an economic?} theory is to "posit a possible structure...to compare to future results" deferring determination of validity to the future. [Q: why is this, then, different from positing a structure and comparing to past results - and determining validity today]? $\endgroup$ – Rusan Kax Dec 15 '14 at 17:10
  • $\begingroup$ right, I meant there is a misconception in general about economic theory. The purpose is to construct models of the market, which verify previous empirical findings and show (in a probabilistic sense, thats the key here) correct indications of future tendencies. While we can't presume to have a General unified Theory, some basis needs to be there to create sensible results for policy making, hence flawed models like the DSGE, no arbitrage, efficiency. Usually, the way a theory, say evolution works, is it fits previousn findings and then holds for future ones, thereby determining its validity. $\endgroup$ – Drew Dec 15 '14 at 18:48
  • $\begingroup$ Validity cant be determined merely by a past fit, because it would subject to a lot of problems that overfit models are. But rather, a theory has to be general enough to encompass all that has happened and leave room for the dynamics to change and a deeper understanding, ala evolution. Does that make sense? I guess, the question is too general. Yes, one theory has not explained all the things in the market, but the market helps us update these theories in the correct direction at least. But like I said, if there is a GUT to be found, it will almost certainly be embraced. $\endgroup$ – Drew Dec 15 '14 at 18:50
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Classical economics cannot "explain" volatility smiles, but neither does it preclude their existence. Economics is far more abstract than financial "quant"modeling and answers very different questions. In the more abstract framework of economics, volatility skew, mean reverting volatility, bubbles, and crashes are all conceivable scenarios. Auto-correlated returns, on the other hand, would likely be un-explainable by classical economics (indeed, their existence "in the long run" is prohibited).

I'm somewhat surprised at your aversion to terms like "state dependent utility of investors". Of course utility is state and time dependent. The beauty of financial prices is that it's frequency and availability can give us more understanding of the nature of the state and time dependence of utility.

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  • $\begingroup$ Thank you for your reply, which is +1'd. Yes, I realize that one answer is: perhaps economics is not the correct place to search for answers to those questions. My aversion was not to state dependent, but to utility of representative investors. The intellectual implication (in the paper) seems to be one can take a really bad idea (representative agent) and make it good by adding on some form of complication (state dependent utility). Your answer also made me think of things classical economics is good for. But that is another question. $\endgroup$ – Rusan Kax Dec 14 '14 at 14:42
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If you call "classical" what is usually tagged as "neoclassical mainstream", then perhaps the answer is no. From the other hand behavioral finance is long time ago became widely accepted and taught, together with cascades stories a-la Hirshleifer. So in wider sense, economics has long ago explained observed deviations from standard theory.

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  • $\begingroup$ Classical, neo-classical...old testament, new testament. $\endgroup$ – Rusan Kax Dec 12 '14 at 20:19
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As I don't really understand your question except for the volatility smile:

Here is a presentation about how the volatility smile flattens as computational precision increases: http://www.rinfinance.com/agenda/2013/talk/Chance+Hanson+etal.pdf the intuition there is that the smile may be the result of computational error.

I would look at agent based approaches of modelling markets and tinker with risk aversion parameters, depending on your modelling approach you can replicate crashes/tails/volatility increases/decreases in the market clearing price.

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