"Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way."
The book covers such things as Brownian motion, completeness of quantum mechanics and the possibility to apply quantum mechanics outside physics. Martingales and fake probabilities and naturally a section on arbitrage and negative probabilities. Further such topics as price and superposition of values, q-calculus in finance, the Implications of the non-Hermiticity of a Black-Scholes Hamilton operator, what is that?
This book clearly has some out of the box thinking!
Since early 1900 we have known that one or two big price movements empirically make the distribution highly non-gaussian (Ignored by most academics and blind followers). Based on this we know that no matter how good mathematical model you have you cannot accurately predict the tail probabilities. And these tails have BIG IMPACT. The solution is to focus on robustness in your hedge, reduced leverage etc. (there is much more to this, time will tell)
From the Basel (May 2012) report:
"Moving from value-at-risk to expected shortfall A number of weaknesses have been identified with using value-at-risk (VaR) for determining regulatory capital requirements, including its inability to capture “tail risk”. For this reason, the Committee has considered alternative risk metrics, in particular expected shortfall (ES). ES measures the riskiness of a position by considering both the size and the likelihood of losses above a certain confidence level. In other words, it is the expected value of those losses beyond a given confidence level. The Committee recognises that moving to ES could entail certain operational challenges; nonetheless it believes that these are outweighed by the benefits of replacing VaR with a measure that better captures tail risk. Accordingly, the Committee is proposing the use of ES for the internal models-based approach and also intends to determine risk weights for the standardised approach using an ES methodology."
"Shortcomings of the models-based approach: The metric used to capitalise trading book exposures was the 10-day value-at-risk (VaR) computed at the 99th percentile, one-tailed confidence interval. By construction, this is a measure aimed at capturing the risk of short-term fluctuations in market prices. While a 10-day VaR might be useful for day-to-day internal risk management purposes, it is questionable whether it meets the objectives of prudential regulation which seeks to ensure that banks have sufficient capital to survive low probability, or “tail”, events. Weaknesses identified with the 10-day VaR metric include: its inability to adequately capture credit risk; its inability to capture market liquidity risk; the provision of incentives for banks to take on tail risk; and, in some circumstances, the inadequate capture of basis risk. Perhaps more fundamentally, the models-based capital framework for market risk relied on a bank-specific perspective of risk, which might not be adequate from the perspective of the banking system as a whole. The pro-cyclicality of VaR-based capital charges based on recent historic data and the large number and size of backtesting exceptions observed during the crisis serve to highlight regulatory concerns with continued reliance on VaR."
I have not met that many naive VaR followers at the trading floor, but yes around in different corporations there are in particular plenty of management removed from the trading floor (taking the big decisions) , often with lack of knowledge about trading and market behaviour that on their desk wants to have simple risk numbers, giving them the whole picture, rather than "scary" worst case scenario think thank discussions with their senior traders. I guess they prefer VaR as a flawed risk benchmark rather than have to tell to the share holders they could go bust in this and that extreme scenario that happen every 20, 50, 100 year (?) (rather than every 2000 years as predicted by their naive VaR models). Or even better reduce the firms over all risk exposure, stop giving loans without any equity behind it etc. And yes there are plenty of academics naively thinking it is just to have the right mathematical model and they can calculate the exact probability for extreme events. Think again!
The case went all the way to the Supreme Court where the student and the other private investor won with lowest possible margin (3 against 2 in votes). I do not know the case in detail, but it sounded strange that someone should get imprisoned for making the markets more efficient by figuring out the pattern of a clearly not so smart algorithm. Should it not be the firm building the not so clever algorithm that simply should stop using it, or keep loosing money. I would think we need more such clever students, then yes may be the scary (?) HFT algorithm trading would slow down a bit. When human brain power pick money from the machines someone would possibly push the slow down bottom on their algorithm?
Coins are physical metal with embedded put options, typically issued deep-in-the-money, but have in recent times for several circulating US coins been going from deep in-the-money to out-of-the-money to in-the money again.
Some people probably took advantage of certain arbitrage opportunities in US coins back in 2006. As described in the paper in the end of 2006 the US mint changed the rules and knocked out part of the option element in coins.
For precious metal coins the put option is on the other hand typically issued far out-of -the-money.
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
"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.
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.
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