On Black-Scholes-Merton and time machines
October 30, 2008
The discussion about the performativity of economics in OrgTheory is continuing . This new chapter includes Ezra Zuckerman, myself and the introduction of a time travelling machine! In other words, what would have Black, Scholes and Merton said if they were able to see, in 1973, the future of their model. I’m biased, of course, but I think that this is a fun and thought-provoking little piece.
Yuval, I’m not sure it is so productive to get into an extended discussion about the use of BSM as a canonical case by which to push on the idea that economic theories are performative. I’m pretty sure that we are not going to agree on this. Here is a quick summary of my view (and that of a financial economist friend of mine, who gave me some feedback on this):
Let’s say that we traveled by time machine to 1973, and we reported to Black, Scholes, and Merton that: (a) their model was an inaccurate predictor of prices in 1973; (b) that it would become highly accurate by 1980; and (c) it would become less accurate by 1987. Here is how I think they would respond:
1. We know it’s not accurate today. This doesn’t surprise us since it’s a *new* model of what the option price *should be*. It is not a model of what prices are. Moreover, it’s a very good thing it is inaccurate today! This means that you, my friend, can make a lot of money by using it! That is, it is a valuation *tool.* If you use it, you will become rich! And *those profits* vindicate our model! (Of course, we don’t rule out the possibility that there are better models, which would be even more profitable. We know that our model is based on highly restrictive assumptions. But it’s still a much better model of what prices should be than any other model we currently have).
2. Of course, once word gets out that this is the right way to value options, everyone will adopt it and then use of our model will no longer provide profit opportunities. So, the fact that you tell me that it will become accurate by 1980 is yet another *vindication* of our tool!
3. You then tell us that, after 1987, it will become less accurate. Ok, well that could concern me. But let me ask you. Is it also true that:
(a) The models of the future are all built on our basic foundation [with its key insight, which is that option prices are driven by the volatility of the underlying asset], but just relax our highly restrictive assumptions [which we already know are too restrictive but hey, we have to start somewhere!]?
(b) That our model would still be the convention because none of its descendants had won out to replace it as the convention? and
(c) That people will be assessing the state of the financial system with a volatility index whose logic derives from our model?
What? These things will also be true? Wow. That is the ultimate vindication. After all, we know that our model will be improved upon. What would worry us would be if our basic foundation were undermined, and it sounds like that has not happened. Moreover, we recognize that point 2 above need not be a vindication of our model. Rather, the fact that a valuation tool becomes more and more accurate could just reflect the fact that it has become widely adopted (in fact, we have been told that in the future, some finance scholars will find out that this is true even for models that have nothing to do with fundamentals! [see http://ksghome.harvard.edu/~jfrankel/ChartistsFunds&Demand$%20F&F88.pdf. But the fact that our model is still basically accurate and that all future models are built on its foundation indicates that our model was not just a self-fulfilling fad, but was actually a great model. (We hear that this basic point will be made in a paper by Felin and Foss.)
Ezra, this is a fascinating discussion! Also, I love the time machine metaphor!
But, before I answer to the hypothetical future-aware B, S & M I would like to say that I agree with you about not turning the Black-Scholes-Merton model into a ‘canonical case’ of performativity. While it is an interesting case, because of the natural experiment setting, there are other, equally promising cases out there (e.g. target costing, fair value in accounting, balance scorecards).
Now, for Black, Scholes and Merton. Yes, your model is inaccurate now, in 1973, and it cannot be accurate, because the assumptions that underpin it do not exist in the market (no-restriction short selling, free borrowing, continuous trading, etc). And yes, people will use the model (to begin with, your sheets with calculated prices, Fischer Black) and will make nice profits. This, as you say, is a nice vindication of the model.
But, in your second point you start talking sociology, I’m afraid and less financial economics: the fact that people will adopt the model and thereby change prices towards its predictions is a vindication of your theory? Where in your model do we see a description of such mimetic social behaviour? Don’t tell me that Chicago U in the 1970s is a hub of behavioural economists!
Your third point sings your praises, and rightly so, because you guys, transformed financial markets (some would say even capitalism) and virtually invented modern financial risk management. Right again, mainstream risk management models are built on the principles of Black-Scholes-Merton. But, we you start talking about ‘the convention’ I think that you actually refer to more to how the model will be used and how it will become ‘institutionalised’, put into software and rules and regulations, rather than its theoretical basis. The convention that Black-Scholes-Merton is the best model in existence will be built, step by step, by a variety of economic actors: trading firms that used implied volatility as an intra-organisational coordination, the options clearinghouse, the SEC and many other exchanges across the world.
And, yes: you are right to assume a causal connection between adoption and increased accuracy – this process is now called performativity of economics. That is, you will an explosive success (including one very nice surprise in 1997!), but this success should be attributed, in large part, to how your model will affect its environment. Your model, like many other bits of expert knowledge, played a central role in a process of performative institutionalization – it helped to bring about the institutions that performed its accuracy. No doubt – it is a great model – but markets are not detached from the theories describing them and your model will be a vital part of the market.