Methods for pricing options in the 19th century

George Dotsis 09 September 2017

a

A

The story of Thales in Aristotle's Politics is widely cited in the finance literature as perhaps the first event of option trading in antiquity. According to Aristotle, Thales made a fortune from buying a call option on the rental price of oil presses. The option gave Thales the right to rent oil presses at a predetermined price and “when the season arrived, there was a sudden demand for a number of presses at the same time, and by letting them out on what terms he liked, he realised a large sum of money, so proving that it is easy for philosophers to be rich if they choose, but this is not what they care about”.1

A short history of option contracts

Sea loans or bottomry loans were early forms of financing with embedded options. Bottomry loans were the typical source of maritime financing in the ancient world and especially in ancient Greece. They were made to merchants and ship owners for financing the transportation of goods using the vessel and/or the cargo as collateral. The payment of the loan was contingent upon the successful arrival of the ship at the destination harbour. In the event of a shipwreck, the borrower did not bear any liabilities with respect to the repayment of the loan. Bottomry loans were not plain loans since the lender was exposed to the risk of the voyage, nor a type of partnership since the return of the loan was fixed and known in advance. From the perspective of Merton's (1974) formulation for the valuation of corporate debt, the bottomry loan is economically equivalent to riskless lending and a put option written by the creditor on the value of the vessel and the cargo. That is why bottomry loans are often referred to as early forms of ship insurance.2

According to the historical evidence (Poitras 2009), exchange trading in standalone equity options first began in the Amsterdam bourse in the 17th century. In the Amsterdam bourse, there was an active market of derivative contracts whose underlying asset was the stock of the Dutch East India Company. The Dutch East India Company was perhaps the first limited-liability joint-stock company and the first company in world's economic history to perform an initial public offering and issue negotiable shares sold to the wider public. Stock and option trading gradually moved to London after the Glorious Revolution, and in 1773 the London Stock Exchange was formally established. At that time, derivative trades were often called ‘time trades’, ‘time bargains’ or ‘jobbing trades’ (Harrison 2003). Following the events of the South Sea Bubble in 1720, in 1734 the English parliament passed Sir John Barnard's Act, which was a set of rules aimed to prevent stock jobbing, and trade in options and forwards was forbidden. Despite the fact that time trades were in general unenforceable by law and often explicitly banned, the market for these contracts continued to grow. An active over-the-counter market for equity options developed in New York after the civil war.

Mixon (2009) examines equity option data from the US over-the-counter market in the 1870s and finds that many of the empirical regularities observed in modern option markets regarding implied volatility and implied skewness were also present in the options market of the 19th century. He concludes that “traders in the nineteenth century appear to have priced options the same way that twenty-first-century traders price options”. This is a fascinating result that leads naturally to the following question – what type of pricing techniques did investors in the 19th century use?

Put-and-call by Leonard R. Higgins

Higgins was an option trader in London and in his book Put-and-call he describes the option pricing methods and option strategies used in the late 19th century in the City of London.3 According to Higgins (1906: 58), in the late 19th century the London market was the option market par excellence of the world since “nowhere the same facility for giving and taking, for operating in long and short options, and for hedging against a favourable put or call in the firm stock as that which exists in London. It rarely happens that an option is done in the Paris market for more than one month ahead, and in Berlin too the majority of such dealings are arranged for a similar period. In London two and three months’ calls are easily negotiated in the active stocks”.

In a recent paper, I examine thoroughly Higgins’s book through the lenses of modern option pricing techniques (Dotsis 2017). I show that investors in that period had developed sophisticated option pricing techniques for determining the prices of at-the-money, slightly out-of-the-money and in-the-money short-term calls and puts, and used routinely the put-call parity for option conversion and static replication of option positions.

The option contracts analysed in Higgins's book could be exercised only at maturity (European-style). They were written on the forward price of the underlying asset, the time to expiration ranged from 15 days up to 90 days and premiums were paid at expiration. The term ‘put-and-call’ which is used repeatedly in Higgins’s book, and is also the title of the book, refers to an at-the-money-forward straddle. The at-the-money-forward straddle is a portfolio of a call option and a put option with the same expiration date and an exercise price equal to the forward price of the underlying asset. The put-call parity dictates that the at-the-money-forward call and the at-the-money-forward put option prices have to be equal to preclude arbitrage opportunities.

The pricing approach described in Higgins's book could be summarised as follows. First, traders were pricing short-term at-the-money-forward straddles with 30, 60, or 90 days to maturity. The prices of the at-the-money-forward straddles were expressed as a percentage of the forward price of the underlying asset and were computed as the risk-adjusted expected absolute deviation (Higgins uses the term ‘average fluctuation’) of the underlying price from the strike price at expiration. It is interesting to note that the computation of the at-the-money-forward straddle price as the risk-adjusted estimate of future absolute deviation emerges naturally from the payoff function itself.

Figure 1 The payoff of an at-the-money-forward straddle with strike price F

The expectation of the absolute deviation was based on historical estimates plus a risk premium for future uncertainty as well as some other mark-ups. According to Higgins (1906: 70-71), some of the basic rules for finding the price of the at-the-money-forward straddle were, “[f]irstly, to ascertain the past average fluctuations over a considerable period of time of the stock to be operated in. Secondly, to consider whether there is any special influence at work calculated to modify that average result in the immediate future (such as a particular scarcity of the stock for delivery, financial strain or probability of political complications).” Higgins is using the at-the-money-forward straddle prices as reference points in a linear approximation formula, which is based on the put-call parity, to price slightly out-of-the-money and slightly in-the-money put and call options. In Higgins’s book, the in-the-money and out-of-the-money options are called ‘fancy options.’ In my paper, I show that the approximation used by Higgins is analogous to a first-order Taylor expansion around the out-of-the-money straddle price.

From Higgins’s pricing approach, it appears that option traders in the late 19th century did not consider the expected return of the underlying asset to be a parameter that had a direct impact on option prices and viewed options mainly as instruments for trade volatility. Higgins (1906: 9) writes that, “[i]t may be worthy of remark that ‘calls’ are more often dealt in than ‘puts’, the reason probably being that the majority of ‘punters’ in stocks and shares are more inclined to look at the bright side of things, and therefore more often ‘see’ a rise than a fall in prices. This special inclination to buy ‘calls’ and to leave ‘puts’ severely alone does not, however, tend to make ‘calls’ dear and ‘puts’ cheap, for it will be shown in a later chapter that the adroit dealer in options can convert a ‘put’ into a ‘call’, a ‘call’ into a ‘put’, a ‘call o’ more’ into a ‘put-and-call’, in fact, any option into another, by dealing against it in the stock.”4

Summary

Modern theories of option pricing are based on continuous-time stochastic processes, deductive reasoning and a hypothesis of frictionless and perfect markets and provide a pricing mechanism that fits the full cross-section of call and put option prices. From Higgins’s book, it appears that option traders in the late 19th century used inductive reasoning, interpolation techniques and empirical methods and were able to determine quite accurately the prices of at-of-the-money and slightly out-of-the-money and in-the-money short-term calls and puts. Option traders in the late 19th century priced at-the-money-forward straddles the same way option traders in the 21st century price them – as risk-adjusted estimates of future stock fluctuation. The difference is that modern option traders measure stock return fluctuation using the concept of variance and standard deviation while option traders in the late 19th century measured stock return fluctuation using the mean absolute deviation. Higgins’s book shows that practitioners in the late 19th century had developed sophisticated methods for determining option prices almost a century before the seminal work of Black and Scholes (1973) and Merton (1973) and the advent of computer power.

References

Baskin, J B and P J Miranti (1997), A history of corporate finance, Cambridge: Cambridge University Press.

Black, F and M Scholes (1973), “The pricing of options and corporate liabilities”, Journal of Political Economy 81: 637-659.

Cohen, E E (1992), Athenian economy and society: A banking perspective, Princeton: Princeton University Press.

Dotsis, G (2017), "Option pricing methods in the late 19th century", available at SSRN.

Harrison, P (2003), The economic effects of innovation, regulation, and reputation on derivatives trading: Some historical analysis of early 18th century stock markets, Federal Reserve Board Report.

Higgins, L (1906), The put-and-call, Aberdeen: Aberdeen University Press.

Merton, R C (1973), “Theory of rational option pricing”, Bell Journal of Economics and Management Science 4: 141-183.

Merton, R C (1974), “On the pricing of corporate debt: The risk structure of interest rates,” Journal of Finance 29: 449-470.

Mixon, S (2009), “Option markets and implied volatility: Past versus present”, Journal of Financial Economics 94: 171-191.

Poitras, G (2009), “The early history of option contracts”, in Hafner, W and H Zimmermann (Eds.), Vinzenz Bronzin’s option pricing models: Exposition and appraisal, Berlin and Heidelberg: Springer Verlag.

Endnotes

[1] Translation by H. Rackham (1944), available at the Perseus Digital Library here.

[2] Cohen (1992) examines sources from Demosthenes and Lysias and argues that yields probably varied between 12.5% and over 100%. Baskin and Miranti (1997) and Cohen (1992) provide a compelling explanation based on asymmetric information and information costs as to why these contingent claim contracts were so widely used in maritime trade. They argue that these type of arrangements minimised investors’ information requirements. If the bottomry loans did not embed the cancellation provision, lenders would have to spend time and effort to collect accurate information with respect to the financial viability of the borrowing merchants.

[3] The book is available online here: https://archive.org/details/putandcall00higguoft.

[4] The ‘call o’ more’ or ‘put o’ more’ were option contracts that gave the holder the right to repeat multiple times the purchase or the selling of the underlying asset (see Dotsis 2017).

a

A

Topics:  Economic history Financial markets

Tags:  option pricing, call option, put option, at-the-money-forward straddle, 19th century, financial markets, history

Assistant Professor of Finance, National and Kapodistrian University of Athens

Events