Ali’s blog

Mostly quant stuff with occasional digressions

Donald MacKenzie on option theory

Posted by alifinmath on December 28, 2007

MacKenzie is a professor of sociology at Edinburgh. He has put forward some very interesting ideas about the role of option theory in creating the very option market it is supposed to be describing. He came out with a book last year — An Engine, Not a Camera — published by the MIT Press, where he discusses this at length. There’s an earlier paper of his — Option Theory and the Construction of Derivatives Markets — published in 2005, where he argues the same thesis; it’s available here. Some excerpts:

“Implied volatility” is an inherently theoretical notion: its values cannot be calculated without an option pricing model. By simplifing the options markets’ complexity to a common metric, “implied volatility” allowed the burgeoning trading firms of the 1970s, such as O’Connor and Associates, to expand and extend their activities by co-ordinating teams of floor traders operating on geographically dispersed options exchanges. What was being traded on these exchanges, the firms reasoned, wasthe Black-Scholes-Merton model’s fundamental parameter: volatility.

The idea that Black-Scholes-Merton might have created the very market structure it was purporting to describe:

In the case of the Black-Scholes-Merton model, the claim of Barnesian performativitywould thus be the claim that the market practices informed by the model altered economic processes towards conformity with the model – for example, altered patterns ofmarket prices towards what the model postulated – and the model was thus an instance of  “knowledge substantially confirmed by the practice it sustains.”

That this might be the case is suggested by the way in which the discrepancies between model and market seem to have diminished rapidly in the years after the model’s publication in 1973.

And why B-S-M was adopted when its initial correspondence with numbers and practices wasn’t initially that good:

Why might an options market participant in the 1970s have chosen to use Black’s sheets or another material implementation of the Black-Scholes-Merton model? The answer might simply be because the sheets were a good guide to market prices, but, as noted above, the fit between model and market was not always close, especially in the earlier part of the decade. Although it is difficult to be certain of the reasons for the dominance of the Black-Scholes-Merton model, a number of factors seem likely to have been significant. One factor – perhaps the factor closest to Bourdieu’s emphasis on the inter-relations of language, power, legitimacy, and cultural hierarchy – was the authority of economics. Financial economists quickly came to see the Black-Scholes-Merton model as superior to its predecessors. As noted above, it involved no non-observable parameters except for volatility, and it had a clear theoretical basis, one closely linked to the field’s dominant viewpoint: efficient market theory. The Black-Scholes-Merton model thus “inherited” the general cognitive authority of financial economics in a political culture in which economics was a useful source of legitimacy, and in which, in particular, the status of financial economics was rising fast.
Chicago floor traders in general were and are not in awe of professors. From their viewpoint, however, the model had the advantage of “cognitive” simplicity. The underlying mathematics might be complicated, but the model could be talked about and thought about relatively straightforwardly: its one free parameter – volatility – was easily grasped, discussed, and reasoned about. Kassouf’s model, in contrast, was a regression equation with six coefficients that required econometric estimation (Kassouf 1965, p. 55). An options pricing service based on Kassouf’s model would perform the requisite calculations, but from the user’s viewpoint such a model was a black box: it could not be reasoned about and talked about in as simple a way as the Black-Scholes-Merton model could. The many variants of, modifications of, and alternatives to Black- Scholes-Merton that quickly were offered by other financial economists also had a crucial drawback in this respect: they typically involved a mental grasp of, and estimation of, more than one free parameter – often three or more. Another factor underlying the success of the Black-Scholes-Merton model was simply that it was publicly available in a way many of its early competitors were not. As U.S. law stood in the 1960s and 1970s, it was unlikely that an options pricing model would be granted patent or copyright protection, so there was a temptation not to disclose the details of a model. Black, Scholes, and Merton, however, did publish the details, as did Sheen Kassouf (whose model was described in his PhD thesis). Keeping the detail private may have been perfectly sensible for those who hoped to make money from their models, but it was a barrier to the adoption of those models by others.

And how adoption of B-S-M created a closer correspondence between it and the market:

As noted above, with plausible estimates of volatility the Black-Scholes-Merton model tended to generate option values that were below the market prices prevalent in the ad hoc put and call market and in the early months of the Chicago Board Options Exchange. For a critic of the model such as Gastineau, that was an indication that the model undervalued options. However, it also meant that market competition tended to drive option prices down towards Black-Scholes values.

Black-Scholes prices were, in a sense, imposed even upon those writers of options who believed such prices to be too low: they either had to lower the prices at which they sold options, or see their business taken away from them by the adherents of Black-Scholes.

Other reasons for adopting B-S-M:

Assessing the risks being taken by a trader was far from simple: he or she might hold dozens of option positions, and perhaps positions in the underlying stock as well. The Black-Scholes-Merton model’s deltas could, however, be aggregated to a single measure of exposure to the price movements of a given stock. If a trader’s aggregate delta was close to zero, his or her positions were “delta-neutral” and could be considered to a first approximation well-hedged; if the delta was substantial, then his or her positions were, in aggregate, risky. Sophisticated risk managers learned not to stop at delta, but also to consider the other measures colloquially known as “the Greeks,” such as gamma….


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