As I recounted a few months ago, by reading Ghislaine Idabouk's briliant dissertation on the mathematics of options pricing (Black, Scholes, Merton [hereafter BSM] etc) I got inspired to do a weekly blog on philosophy of economics. My main idea was to experiment with philosophic reflection about real economics, and to move discussion away from the Hayek/Friedman vs Keynes paradigm. (During the las few weeks this (d)evolved into bashing Harvard economists here, here, and here.) This week I want to return to the blog's roots. Several of my interlocuters within philosophy, primarily David Hyder and Jared Woodard, have trading backgrounds (or dabble as hedge-fund managers). Their fundamental criticism of my blogging is that traders at most deploy BSM as a heuristic. A very interesting paper, which relies on the distinction between techne and science), makes an even stronger claim: BSM never gets used—although that claim is also contradicted within the paper when they try to show that folk who used BSM sometimes go bankrupt. The paper also provide a useful history on pre-BSM option-pricing techniques (and disputes the originality of BSM). And the authors call attention to the importance of Mandelbrot’s 1960s challenges to the statistical techniques that became the core of the BSM approach. (I had approached Idabouk about a joint paper on exactly that, so we’ve been partially scooped; who knew this is a fast-moving business?)
Amusingly, in line of their distinction, the (high profile!) authors of the article represent themselves as mere craftsmen. (I kind of felt I was reading a 16th century tract in which the high minded theologians are ridiculed by the lowly applied mathematicians.) Now today I want to explore one issue in their paper: the not-so-theorized role of modality in the statistical apparatus (this will be familiar to a number of readers). Later in the week, or next, I will explore in light of their paper and my discussion with Woodard to what degree we are still caught debating these issues in framework set by BSM (and behind it Paul Samuelson's whole approach to these matters).
In their criticism of BSM, Haup and Taleb point out that the way BSM gets used in dynamic hedging, it "requires all moments of the probability distribution to exist." (Something David M. Levy also often insisted to me.) But other than noting that this does not seem to obtain in the empirical world (no small matter!), they don't quite clear on what's going on.
Note, first, that the modality that governs the moments in the probability distribution is, thus, necessity (necessarily all moments exist). Now, recall from my earlier discussion, that modern BSM relies on a martingale to model randomness. (I have criticized the switch from uncertainty to randomness before.) The martingale helps define a trajectory of a stochastic process. And so as we can ask an innocent seeming question: do the set/class of moments that end up in the trajectory have special properties? As David Levy first reminded me, we know the answer is "yes" because it turns out some distributions (median distribution) come naturally, while others (e.g. mean distributions) are ruled out. So, second, this means that the modal property of the values that end up in the trajectory (i.e. not merely really possible as I had suggested before, but necessary) is different from some of the values that could have ended up in the trajectory (merely possible), and those that never could end up in the trajectory (i.e., impossible). Yet, what is completely lacking is a taxonomy of the modal properties of the particular markets in which BSM gets applied. (This is where philosophers may usefully team up with economists/statisticians.)
Now admittedly this goes against the spirt of the paper by Haug and Taleb. They want a return to craftsmanship. I have sympathy for this. But besides the fact that our institutions (of credentialing/hiring/good governance) do not seem to promote this, the mere existence of science changes craft (probably forever); the craftsman loses her autonomy and her thoughts get infected by scientific ideas. The craftsman cannot return to paradise. So, we may as well try to help improve scientific thought (although I do often worry that the solution(s) may be worse than the problems).
Recent Comments