I have for a long time observed how over sensitive many (but luckily not all) academics are to others citing or not citing their work (in the light they prefer). Academic is mainly about getting published in the right journals and get cited by other academics. This is important to become a professor and to get grants and be looked upon as prestigious in the academic world. That others cite your published work naturally make sense, it is irritating when others re-publish your ideas without citing you.
Recently Myron Scholes attacked Nassim Taleb for not citing academics
” Scholes said academics do not take Taleb seriously because he does not cite previous academic literature in his theories, relegating him to a man who "popularizes ideas and is making money selling books."
Full story here:
|Scholes attack on Taleb |
So Taleb is not taken seriously by academics (according to Scholes) because he cites plenty of academics, but not every academic Scholes would prefer in the light Scholes would prefer? The Black Swan has 1350 citations to loads of academics and non-academics. I am sure Nassim always could cite more, we all could. However I find it surprising that Scholes are throwing this stone when he is sitting in a glass house. What about all the academics not citing traders that had published great ideas (that actually was used in practice) long before the academics?
For example Professor Stoll published on the put-call parity in Journal of Finance in 1969 without citing several traders that had published the put-cal parity in greater detail than him long before him. Most academics still citing Stoll as the one that came up with the put call parity. What about Myron Scholes himself, why did he not cite for example Filer (1959), Reinach, (1961), Thorp (1969), Bernhard, (1970), Nelson (1904)..... and a whole series of papers that had been looking at discrete market neutral delta hedging as well as the put-cal parity long before their paper in 1973. There is a whole series of academics that did not cite traders (as well as academics) that published ideas or part of their ideas long before them. Traders normally not care if academic cite them or not, they do not bother to scream about it like some academics do, traders have their income from trading and not from academic jobs where it is publish or perish.
There could of course be many reasons academics do not cite traders, they simply did not know about the sources. Still part of an academic job should be at least to do a good attempt to dig out literature that published central ideas before them, even if this means traveling around visiting a few libraries and dig out some books and papers. My point is not that academics did not cite every trader or ancient academics that came up with central ideas long before them. As researchers dig into the literature it will over time be clear who came up with different ideas first, until time again forget/diffuse the originators of an idea.
My point is simply that academics should be careful throwing stones at traders (that often also are academics) for not citing every possible academics they prefer in the light they prefer, at least not before they start to cite properly themselves, in particular when it comes to great ideas like the put-call parity that was invented long before their time.
Many academics (not all) have a tendency to only look into their own defined prestigious journals for who is who, and for who published what and when, they are not looking for the truth (or if their theories has any link to what actually can be done in the markets), but to publish or perish.
Options have actively been trading for at least 400 to 500 years. Some academics (luckely not all) still think options and derivatives basically got invented in the early 1970s, or that at least traders not could properly price or hedge options before that time. I just got hold of a small option booklet written by
| Professor Dr. Emanuel Leser |
He was a professor in Staatswissenschaft at university of Heidelberg. His booklet was published in 1875. I find it interesting that he is referring to option literature all the way back to the 1600. Another ignored and forgotten German source I got hold of today from a library with high security and a great selection of dusty old books mentions option trading all the way back to 1500.
How can it be that options have traded for at least 400 to 500 years, and that both traders and professors have published actively about them for many hundred years and still some of today’s finance professors think people hardly could price or hedge options before 1973?
More on this and other ignored and forgotten sources later on. Financial Archeology is quite interesting indeed.
Leser, E. (1875): “Zur Geschichte Der Pramiengeshafte”. University of Heidelberg
Mitchell (1915), Oliver (1926) and Mills (1927) empirically all pointed out high-peak/fat-tails in price data.
My favorite quote is from Mills (1927) (it tells it all)
”A distribution may depart widely from the Gaussian type because the influence of one or two extreme price change.”
Mandelbrot went deeper into fat-tails in the early 1960s. Then in the 60s and 70s there was a series of so called great discoveries in academic finance, they all based their models on Gaussian. Empirical facts was pushed under the carpet, this to get every theoretical model consistent with each other (CAPM, Black-Scholes-Merton, Sharpe Ratio etc.)
For example the idea behind the Sharpe ratio was great: to get a simple quantitative measure of risk versus returns. The problem was the way the Sharpe ratio measure risk (sigma alone) was basically useless. To use Sharpe ratio is simply dangerous, still most funds use it as marketing device (for often naiive investors). But it must be better than nothing? Well before the Sharpe ratio researcher evidently at least looked at the whole historical distribution (for as much data they had), far from good but at least better (at least it forced you to think).
Do we need a global credit contraction and melt down of finacial markets to make people once agian rember and understand what Mills and others pointed out in early 1900 ? Everybody on Wall Street claim they understand fat-tails, but from recent market blow ups (from only moderate moves) this do not seem to be the reality....
Mandelbrot, B. (1962): “The Variation of Certain Speculative Prices,” Thomas J. Watson Research Center Report NC-87: The International Re- search Center of the International Business Machine Corporation.
Mitchell, Wesley, C. (1915): “The Making and Using of Index Numbers,” Introduction to Index Numbers and Wholesale Prices in the United States and Foreign Countries (published in 1915 as Bul letin No. 173 of the U.S. Bureau of Labor Statistics, reprinted in 1921 as Bul letin No. 284, and in 1938 as Bul letin No. 656).
Mills F. (1927) The Behaviour of Prices, National Bureau of Economic Research.
Oliver, M. (1926): Les Nombres Indices de la Variation des Prix. Paris doc- toral dissertation.
more details also in my chapter 1: Derivatives Models on Models
Far from a complete list, but here are a list of many important references (some of them have been ignored) to early insight in option pricing and hedging.
1688 De La Vega describes active option market and diffusely the put-call parity. See also Knoll (2004) that points out that put-call parity potentially can be traced back 2000 years.
1900 Bachelier (in his Dr thesis) come sup with first option formula (assuming normal distributed asset), and comes with a lot of mathematical insight in option pricing.
1902/1904 Higgins and Nelson: Market neutral delta hedging for at-the-money options well known. Put-call parity fully known.
1908 Vinzenz Bronzin publish book deriving several option pricing formulas. Bronzin based his risk-neutral option valuation on robust arbitrage principles such as the put-call parity and the link between the forward price and call and put options.
1910 Henry Deutsch describes put-call parity but in less detail than Higgins and Nelson.
1936 W. D. Gann describes market neutral delta hedging of at-the-money options, but in less details than Nelson (1904). Gann also indicates more dynamic hedging.
1956 Kruizenga re-discovered the put-call parity, but in less details than was already described by Higgins and Nelson.
1960 Freid describe empirical realtionships between warrants and the common stock price.
1961 Sprenkle publish option formula assuming log-normal distributed asset price.
1961 Reinach describes how market makers (converters) actively use put-call parity as well as how they hedge embedded options in convertible bonds with options.
1964 Boness describes an option formula basically identical to the Black-Scholes-Merton formula. However he do not argue for risk-neutral valuation based on continuous time delta hedging or the Capital Asset Pricing model.
1965 McKean gives closed form solution for American perpetual options, but not under theoretical risk-neutrality.
1967 Ed Thorp and Kausoff extend market neutral delta hedging to options with any strike (moneyness) or time to maturity.
1969 Thorp points to the direction of dynamic delta hedging, and how it will remove more risk than static delta hedging.
1969 Stoll publish a paper in Journal of Finance describing the Put-Call parity. However there was little nothing new, more was known already in the early 1900.
1970Arnold Bernhard & Co describe market neutral delta hedging of convertible bonds and warrants. Describe numerically how to approximate delta. Publish list of hedge ratio (delta) for large numbers of convertible bonds and warrants.
1973 Black-Scholes (1973) and Merton (1973) referring to Thorp and Kassouf extends delta hedging to continuous time delta hedging. It was a brilliant mathematical idea, but trading is not mathematics. Black, Scholes and Merton naturally knew that continuous time delta hedging not was possible, it was naturally only meant as an approximation. However for an approximation to work reasonably well it must be robust. The idea of continuous time delta hedging is far from robust. Even frequent delta-hedging do not remove enough risk to argue for risk neutral valuation, (see Derivatives Models on Models) for a summary on this topic.
Conclusion: Most robust hedging and pricing principles were basically known before Black, Scholes and Merton. The last step of taking market neutral delta hedging to continuous time delta hedging (or making the model consitent with CAPM) is the only step that not is of any practical use. Even frequent dynamic delta hedging cannot be used as an argument for risk-neutral valuation on its own. More on this in my book Derivatives Models on Models Chapter 2
Delta hedging removes a lot of risk, but not enough to argue for risk-neutral valuation (except in a fantasy world). Non of the traders/researchers describing delta hedging before 1973 ever claimed it could be used to remove all the risk all the time.
Are civilizations gaining of knowledge a stochastic process? The "standard" textbook approach is that our knowledge and science basically more or less have been growing linearly through time.
Looking at the history it looks more like our knowledge at best is a stochastic process with strong(?) positive drift and some big knowledge crashes on the way.
And we only have good knowledge about recent history. When ancient civilizations went under we also to some degree can expect a lot of knowledge went lost, plenty of evidence of this....
Luckily ancient civilizations wrote some of their knowledge down in stone. Today all is paper based and computer disks. If we should get a long period not re-printing our knowledge then most of it would go lost in a few hundred years...
I suggested to my publisher to print my next book in stone, but they refused to listen to me ;-) But at least I presued them to use some good paper quality....My forthcoming book: "Derivatives: Models on Models" is now in for copy editing... a lot of people have asked me about why the title: Models on Models, here are a few reasons for this title:
1. Many of our current moldels are based on ancient ignored and forgotten models.
2. Interview with 16 top modelers from Wall Street and academia...about their view on derivatives and financial models.
3. How we often ignore hidden asumptions in the model behind our model
4. and of course Models on Models (whatever that is, time will show)
The book was much more work than expected (as every book), so will not be out before late this fall October to November.. Sorry will only be in paper edition, no stone edition...but a few of the pages was originally written on material guaranteed to last at least 500 years (canavas). but also this material not used in print edition.
It is impossible to say who discovered something first, Why? Because people like me never publish or even talk about their best ideas, all my Nobel Prize ideas I keep for myself, I can't stand publicity and I hate fame ;-)
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."