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Thread: On financial modelling and the usefulness of wrong theories

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    Educator TheEconomist's Avatar
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    On financial modelling and the usefulness of wrong theories

    I have been meaning to start a broad discussion on financial markets for a while now. I'd like the discussion to involve people with formal training, professional experience and, yes, also people who more or less trade as a personal hobby. It could get technical, but I will try to keep things as simple as possible to encourage as many people as possible to participate.

    My background is almost exclusively in economics, mostly focusing on econometrics. I'm currently taking my first finance course as the last course of my PhD program in economics and you can bet I have to go back and learn a lot of things a typical student already knows ahead of class. Still, it's very interesting and I thought I'd start something very basic to drive a point home regarding the usefulness of models, even in the event that they're wrong as they usually are in some ways. If you want the spoiler, in my experience, models are primarily useful because they help give structure to a discussion.

    Example of a useful bad model
    So, let's pick a model that we know to be very bad in all sorts of ways: the Black-Scholes-Merton model (BSM). This model is used to price European options (contracts that give you the right, but not the obligation to either buy (call) or sell (put) a specific security (the underlying) for a predetermined price (the strike) at a predetermined date (the maturity)). Essentially, it says that the price of an option is a complicated function of the time to maturity, the rate of return you'd get on something like US Treasury bonds, the strike, the current price of the underlying AND the mean growth rate of that security, as well as its volatility (think, the standard deviation over a very short time span). Now, you can measure all those things for something like the S&P500 and compare the BSM prices with the observed prices of option contracts. It performs especially poorly for shorter maturities, as well as on extreme cases (when the underlying price is way above or well below the strike). One very cool thing we can do with BSM is to expressed those mispricing in terms of a pattern of volatility. Essentially, you can ask what must the volatility be for BSM to be correct. That's the implied volatility (IV). If you do it for a given maturity, across all strikes, you can plot this on a figure. If BSM was 100% correct, you'd get a flat line, but what you get is a smile (well, more of a smirk for index options). IV is high on the figure when real option pricces are more expansive than BSM would have it and vice-versa.

    This is an absurdly useful way to think about the problem. Irrespective of the validity of the BSM model, you can always draw a volatility smile using BSM by treating it as just an arbitrary, though convenient one-to-one correspondance between option prices and IV. Once you cast the problem in this space, you can learn a few things:

    1. IV for index options tend to give you a smirk, indicating some kind of skewness;
    2. IV has a term structure (the slope and the level change as maturity changes), so if you're going to think about how volatility changes over time, you might need more than one factor driving the process;
    3. IV is pretty high on deep out of the money puts, so you need some way to increase the likelihood of a large changes;
    etc.

    A lot, a lot of research has been made possible just because it's so much easier to think in terms of IV. It sorts of puts everything on a common footing. It also has a nice economic interpretation because backing out information from option prices combines two things (1) the compensation people demand for undertaking risk and (2) their expectation of what's going to happen. So, yes, the model is wrong because it is way too rigid to capture the subtleties of the data. On the other hand, how it fails tells you a lot about how you can try to improve the situation.

    Other topics of discussion
    Note that I am talking from a theoretical perspective where I impose a no-arbitrage condition (in plain English, it means there is no free lunch in financial markets). The reality seems to be closer to there are some free lunches, but you can rarely take advantage of them. For example, the trades required to take advantage of the problem can be too costly, requires to hold a position for too long or it may offer opportunities that are too infrequent.

    On that front, it would be nice to hear about people who have experience trading and who thought about this a lot. It's one possible tengent. Another would be to think about how something that is ultimately false can nonetheless be very useful.
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    Re: On financial modelling and the usefulness of wrong theories

    Toro?
    To live is to suffer~Fritz Lang

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    Educator TheEconomist's Avatar
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    Re: On financial modelling and the usefulness of wrong theories

    Quote Originally Posted by Moonglow View Post
    Toro?
    It seemed apt that an economist's avatar be a bull -- because, you know, bull markets.
    All people who oppose free speech are trying to sell you snake oil. There is absolutely no exception to this rule.

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