Did efficient options pricing lead or follow the development of the Black Scholes Merton model? Evidence from the interwar London Metals Exchange

by David Chambers and Rasheed Saleuddin (Judge Business School, University of Cambridge)

This research is due to be published in the Economic History Review and is currently available on Early View

 

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.

Untitled
Figure 1. Scatter Diagram of Implied Volatility vs. Historic Volatility of 3-month options on Tin and Copper futures, 1921-31. Source: Chambers and Saleuddin (2019)

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:

David Chambers:
d.chambers@jbs.cam.uc.uk

Rasheed Saleuddin,
Rks66@me.com
@r_sale.

Could fiscal policy still stimulate the economy?

by James Cloyne (University of California, Davis), Nicholas Dimsdale (University of Oxford), Natacha Postel-Vinay (London School of Economics)

 

(Anti)_Jubilee_Souvenir
No means test for these ‘unemployed’! by Maro.
1935 was the Silver Jubilee of King George V. There were celebrations and street parties across Britain. However with the country in a financial depression not everyone approved of the public expense associated with the Royal Family. Available at Wikimedia Commons

There has been a longstanding and unresolved debate over the fiscal multiplier, which is the change in economic growth resulting from a change in government spending or change in taxation. The issue became acute in the world recession of 2008-2010, when the International Monetary Fund led a spirited discussion about the contribution that fiscal policy could make to recovery.

In our research, fiscal policy is shown to have had positive impacts on growth, at least during the period surrounding the Great Depression in Britain. The implications for the potential benefits of fiscal policy in a high-debt, low-interest rate environment – and over a turbulent business cycle – may be significant.

The recent controversy follows the debate over the use of fiscal policy to counter the high level of unemployment in interwar Britain. Keynes argued that increased government spending would raise economic activity and reduce unemployment. In the General Theory (1936), he claimed that the multiplier for government expenditure was greater than unity.

A few more recent studies have confirmed that the multiplier effect is greater than unity for both the interwar and post-war period. But these results may be spurious since a rise in government expenditure that raises income may also result from a rise in income. Thus, changes in taxes and changes in income may not be independent. What we observe is a strong co-movement of GDP and fiscal measures in which it is hard to isolate the direction of causation.

What is needed is a source of exogenous variation, so that the impact of fiscal changes on GDP can be observed. Fiscal policy may take the form of changes in taxes or expenditure. The problems of endogeneity are generally greater for expenditure than for taxes, since it should be possible to find changes in taxes that are truly exogenous.

Romer and Romer (2010) have developed the so-called ‘narrative technique,’ which has been designed to overcome the problem of endogeneity of tax changes. This involves carefully distilling the historical record in order to infer Chancellors’ motivations behind each fiscal policy move, and isolate those that may be seen as more independent from the contemporaneous fluctuations of the economy.

One may thus be able to distinguish, for example, between taxes that arise from a direct will to stimulate the economy, as compared with changes that are more motivated by a Chancellor’s longstanding ideology. The latter may include, for example, a will to improve transport efficiency within the country, or a desire to make society less unequal.

Interwar Britain is a particularly appropriate period to apply this approach, since the potential for fiscal policy was great on account of the high level of unemployment. In addition, this was a period in which Keynesian countercyclical policies were generally not used, in contrast to the use of demand management policies in the post-war period.

By examining changes in taxes in interwar budgets, we have been able to produce a sample of 300 tax changes. These have been classified into changes in taxes that are endogenous or exogenous. We have been able to test the backward validity of our classification.

The outcome of this work has been to show that changes in taxes that are exogenous had a major impact on changes in GDP. The estimated value of the multiplier for these tax changes is greater than unity and as much as two to three. This is in accordance with results reported in post-war studies of the United States and a study of tax changes in post-war Britain (Cloyne, 2013).

In contrast to earlier work on measuring the multiplier, we concentrate on changes in taxes rather than changes in government expenditure. This is done to reduce problems of endogeneity.

While Keynes argued for using government spending to stimulate the economy, it was only when post-war fiscal policies were being formulated that the potential benefits of fiscal policies via changes in taxes were recognised. While this research does not argue in favour of tax changes over spending policies, it provides evidence that tax policy is a relevant part of the policy toolkit, especially in times of economic difficulty.

Keynes and Actual Investment Decisions in Practice — The NEP-HIS Blog

Keynes and Wall Street By David Chambers (Judge Business School, Cambridge University) and Ali Kabiri (University of Buckingham) Abstract: This article examines in detail how John Maynard Keynes approached investing in the U.S. stock market on behalf of his Cambridge College after the 1929 Wall Street Crash. We exploit the considerable archival material documenting his […]

via Keynes and Actual Investment Decisions in Practice — The NEP-HIS Blog