by David Chambers and Rasheed Saleuddin (Judge Business School, University of Cambridge)
In early 1998 a nervous options trader was asked to fill an order from one of the world’s largest global investors. The fund’s manager, believing that Canadian short term rates would fall in the very near future, wanted to buy the option – but not the obligation – to buy two year bonds for the next two weeks at a ‘strike’ price of 103 per cent of par when they were actually trading at 102. If rates fell enough upon the option’s expiry in two weeks, the bond would trade above 103, and the hedge fund would pocket the difference between the actual price and the strike of 102.
The average volume in options on these bonds for the week was probably a few hundred million dollars of par value, but this client was looking for options on $2 billion. It would be impossible for the trader to find the exact matching trade in the market from another client, and he would have to ‘manufacture’ the options himself. How, then, to calculate the price?
The framework for this analysis was largely developed by Fisher Black, Myron Scholes and Robert Merton, as published in 1972 (Black and Scholes 1972, Merton 1973). But one crucial input into the so-called Black-Scholes-Merton (BSM) model was difficult to estimate: expected future volatility (as measured by standard deviation of returns) of the underlying bond over the next two weeks. The trader looked first to the recent past: What had the two-week volatility been over the past few months? The trader also knew that unemployment numbers were due out in three days and that some uncertainty always surrounds such a release. In the end, the trader used the BSM model and a volatility input of slightly higher than the past two weeks’ observations to account for the uncertainty in unemployment and the large size of the trade. Upon execution, the trader then used the BSM model to calculate the amount of the underlying bond to sell short to hedge some of the risks to the original trade. That trader was one of the co-authors of an article — ‘Commodities option pricing efficiency before Black, Scholes and Merton’ — recently published in the Review. In this study, the authors David Chambers and Rasheed Saleuddin examine a commodity futures options market for the interwar period to determine how traders might have made markets in options before the advent of modern models.
It is often thought that market prices conform to newly-implemented models rather than obeying some natural laws of markets before such laws are revealed to observers. It has been suggested that equity options, specifically, were ‘performative’ in that they converged to BSM-efficient levels shortly after the dissemination of this model in the early 1970s (MacKenzie and Millo 2003). On the other hand, some claim that it was the advent of liquid exchange trading around the same time that led to BSM efficiency (Kairys and Valerio 1997).
Evidence of efficient pricing before the 1970s is sparse and mixed. There are very few data sets with which to test efficiency, and the few that have been used are far from ideal. Two papers (Kairys and Valerio 1997, Mixon 2009) use one-sided indicative advertised levels targeted to retail investors, without any indication that these were prices upon which investors traded. Another paper uses primarily warrant data, yet the prices of warrants, even in modern times, are often far from BSM efficient, for well-understood reasons (Veld 2003). In any event, these studies find that, on average, prices were far from BSM efficient levels. There is little attempt in this early literature to determine if prices were dependent on the most important BSM model parameter –observed volatility.
This study uses a new data set: prices at which the economist John Maynard Keynes traded options on tin and copper futures traded on the interwar London Metals Exchange. In turns out that Keynes traded at levels that were – on average – as efficient as modern markets. Additionally, the traded prices appear to have varied systematically with the key input to the model, observed volatility (Figure 1), with 99% significance and very high R2.
How was it possible that Keynes’ traders and brokers were able to match BSM efficient prices so closely? There is some suggestion that options traders in the 19th and early 20th centuries well understood options theory. Indeed, Anne Murphy (2009) had identified a perhaps surprising degree of sophistication and activity among the options traders in 17th century London. Certainly, by the turn of the previous century, options traders had a strong grasp of many of the fundamentals of options trading and pricing (Higgins 1907). Yet current understanding of the influence of volatility of the underlying asset was still in its infancy and several contemporary breakthroughs in theory were not disseminated widely. Finance scholarship hints at one possible explanation: For options such as those traded by Keynes, the relationship between the key BSM valuation parameter, volatility, and option price are quite straightforward to estimate (Brenner and Subrahmanyam 1988). It may have been the case that market participants were intuitively taking into account BSM without an understanding of the model itself. This conclusion is, of course, pure speculation – but perhaps therein lies its fascination?
To contact the authors: