The Black-Scholes-Merton formula debate keeps rolling, our wilmott blogger
|Pablo Triana has interesting article in Forbes |
I have to say the invention of continuous time dynamic hedging was original, but to go from discrete delta hedging to continuous delta hedging is something traders not can use. Loads of quants keep using the continuous delta hedging argument to model everything in risk-neutral world where supply and demand for options themselves do not enter the equation. Yes I am sure it works well on the University campus, but how many options are trading there?
Yes and option formulas existed long before Black-Scholes-Merton. There is also a book in production I understand that will translate some of the less known "ancient" option formula texts into english.
Here an interesting paper I just came over (thank you Koekebakker for showing me this) indicating empirically that option traders very well could price options before 1973
| Option Markets and Implied Volatility: Past versus Present by Scott Mixon, Societe General |
"Traders in the nineteenth century appear to have priced options the same way that twenty-first century traders price options. Stylized facts relating implied volatility to realized volatility, stock prices, and other implied volatilities, are the same in both eras. This paper quantifies how pricing efficiency of the market has evolved over time: implied volatility is more responsive to realized volatility shocks, and the market’s required compensation for being short volatility declined as the market has matured. Modern pricing models and centralized exchanges increased trading activity, but they did not fundamentally alter pricing behavior in the option market."
As we know from Nelson the put-call parity was fully known at least by 1904 (probably much earlier) the same was discrete market neutral delta hedging for atm options, discrete delta hedging was developed further by several other researchers. Several option formulas existed in early 1900. It comes as no surprise that traders could price options very well before 1973, and now the empirical research seems to confirm this.
But I am sure there was option traders blowing up back then as well as now. Great option traders relay on robust hedging principles and not fantasy assumptions that do not hold in practice. In practice we have jumps, liquidity can dry up, both for underlying and not to forget for the options themselves. For example Nelson indicated great option traders that survived in long run tended to be long options not short. To be long options is a simple way to make your portfolio robust from the massive leftover risk even after market neutral delta hedging is taken into account. Hedging options with options is another way to do this. See also Models on Models chapter 2 for details on this.
Reading more and more "older" texts on finance it seems like people where very open minded in the 1800, early 1900 and until the 1970s:
In 1960 people wrote about "the velocity of the stock's price movement' , about the 'mass associated with the price change' about the 'kinetic energy in stock transactions' etc. (Joseph Whyler)
In early 1900 Henry Moore a Professor of Political Economy at Columbia University was investigating the possibility of planetary impacts on business cycles. He was also detecting high-peak and it looks like fat-tails in price data (cotton) in 1917, but was basically ignoring it. (Fat-tails in price date was known even earlier).
Most people (and all quants) would laugh at this now (planetary impact on business cycles), I did also to begin with, but it is not as stupid as you would think. At least no more removed form reality than assuming continuous time delta hedging to remove all the risk all the time, something many university professors in finance takes deadly serious, especially if they never have worked for a investment bank or trading firm.
Quant finance is in a ongoing crisis and I think we need to open our minds to get forward. I think a very very ancient and dusty text I just got hold of could be a lead in the right direction, more on this later, 2010.
It is soon 2008 Open Your Mind, Open Your Mind!
Some years ago I included the name ’quant’ in a paper submitted for publication. We got it in return and was told that the paper basicaly was good for publication, but we had to remove the word ’quant’ as it was not in the english vocabuary. We did so and got it published. There are now several finance (quants) books with QUANT in their title. And "everyone" seems to want to become a quant these days (except traders).
I was at a Halloween party a few days ago (even if Halloween officially is night of October 31). Most people were dressed up in costumes, but there was a few people that looked very casual and kind of geeky-nerdy, I keep wondering if they actualy had dressed up as quants or if they were real quants? but I did not ask them as I was off-quant duty that evening.
As a Doctor I feel we still have a long way to go in quantitative finance before we get a real science, (see also Derman’s blog), to get there we will potentially need to carry out some surgery first. That is before we potentialy can take the next big step we need to accept that we have several theories that need to be replaced by something much more fundamental.
Most of today’s finance theories remind me of medicine 100 years ago (and to some degree of how medicine still is practiced). In finance we specialized on study and model the symptoms of the market. There is “nothing” directly wrong with this. We had to start out with something. If a doctor knows the symptoms of cold and tells the patient to stay warm and relax, this is often exactly what is needed.
If we know the cold is generated by a particular bacteria we can study it and find ways to kill it in a hopefully efficient manner. We now suddenly have more powerful tools of handling the situation, and we also understand the situation from a much deeper level. Finance is in strong need for a more fundamental understanding of what causes the symptoms. Some attempts has been done on this topic, but so far they have all “failed”. We need new and deeper theories. This will not necessary replace our symptom theories; but will add a lot of power and understanding to our current symptom theories. One of the best remedy for cold is still to stay warm and drink something warm, antibiotics is not necessary recommended. But in finance we have not yet even discovered the antibiotics, but we will!
Well to compare with medicine is not really fair, they have got deeper than symptoms studies but how much medicine is not practiced (and also research) is done wrong because most doctors have zero clue about probability theory…. I bet the truth is scary
Quantitative finance probably has the most advanced symptom theories of any scientific discipline, but we still need to also understand the more fundamental principles of finance. We need something fundamental, a place to start is possibly to go very deep, and build the theories form that level? The future will tell, or should I say the future will possibly tell us once again, knowledge possibly comes and goes in a sequence and in alternation.....
"Since the matter and substances of things are indestructable, all parts are subject to all forms, so that Each and Everything becomes Everything and Each, if not at one and the same time in a single minute, then at various times and various moments, in a sequence and in alternation" Giordano Brune 1584