The Discovery of The Put-Call Parity
Well of course what you keep for yourself do not count in the world of publish or perish, so here let us concentrate on published discoveries: by digging into old forgotten books and papers we can at least try to get a good idea on who published something first.
The put-call parity is by todays researchers typically credited fully to Stoll (1969) Journal of finance, it is a great paper by the way!. But by digging deep into my basement that are filled with heavy weights and a large number of boxes filled with dusty books, most of them published long before my birth I found out something interesting (?). First of all the discovery of the put-call parity seems to be over multiple steps, well this is kind of known. Almost no great discovery is out of the blue.
Second it seems like a forgotten and ignored option trader (Converter): Anthony M. Reinach was the first one to fully understand and publish the put-call parity:
1688: THE DIFFUSE START: DE LA VEGA
Descibes somewhat diffusly what probably can be considered knowledge of put-call parity for options on forwards
"We say of those who buy means of a forward call contract and sell at fixed term or of those who sell by means of a put contract and buy at a fixed term that they shift the course of their speculation"
Seems like this is conversion of call into put or put into call on options on forwards.
1900: THE DIFFUSE START: BACHELIER
In his Dr. thesis of March 19, 1900 Bachelier describes the purchase of a future contract against a short call and draw the profit and loss (P&L) diagram at maturity that clearly shows that this has same payoff profile as what we would call a put, this can be seen as the first diffuse description of the put-call parity....but it is not at all clear that he understood the full implications of this.
1956(1964): VERY CLOSE: KRUIZENGA
Kruizenga in his Dr. thesis at MIT 1956 (first published in 1964 in Cootners book) describes what must be considered a very good understanding of the main principle behind the put-call parity, to offer a few quotes;
“Buying a call plus selling short is equivalent to buying a put”,
“Writing a put and buying a call is equivalent to buying the stock”.
Kruizenga also describes a large number of examples of transforming one option strategy into another one basically using the put-call parity. Kruizenga is however not describing the importance of taking into account the funding cost of going long or short the shares as one need to do when using the put-call parity for options on stocks as he do.
1961: FULLY UNDERSTOOD: REINACH
Antony M. Reinach was a Converter at the New York Stock Exchange, not only did he operate as a Converter but he also published details about what the Conversion business was all about . In his book “The Nature of Puts & Calls” New York, The Bookmailer Inc.: he in detail describe the conversion business. Conversion is what today is known as the put-call parity. The conversion business was fully based on conversion (that is the put-call parity). Converters were traders or firms specializing in hedging their risk and supplying options using conversion (put-call parity)
From his book it is clear that Reinach fully understood the put-call parity, he fully understood why calls on stocks with same strike price as a put had to be more expensive than the put, the reason is the funding cost of the share when transforming a put + a stock into a call. Reinach shows a calculation example of this, that is exactly equal to the put-call parity as we know it today.
From his book it is also clear that he knew that put-call parity did not hold fully for American options. He describes how Converters sometimes can take advantage off this. In particular by buying puts + stock and turning them into calls that they sold to call buyers. Then if call holder exercised the calls prematurely the Converter is left with some value in his puts for free.
As Reinach actually was actively trading as a Converter he also describes details like taking into account transaction costs.
A very interesting quote from Reinach book is
"Although I have no figures to substantiate my claim, I estimate that over 60 per cent of all Calls are made possible by the existence of Converters. Without Converters, in other words, the Put & Call business would virtually be extinct"
In other words Converters supplying the market with options at that time was hedging away almost all risk by other options. The put-call parity is very robust and is one of the strongest arbitrage principles, it is interesting to see how actively it was used, and not to forget how important it still is.
Anthony Reinach knew of several other robust hedging "tricks" most of them involving options against options, here is a well known one, but published already back in 1961:
"Writers and traders have figured out other procedures for making profits writing Puts & Calls. Most are too specialized for all but the seasoned professional. One such procedure is the ownership of a convertible bonds and then writing of Calls against the stock into which the bonds are convertible. If the stock is called , the bonds are converted and the stock is delivered."
