We don’t know the past, present or future, and we don’t even know the probabilities of the past present or future.
I was out rowing today I told my friend. "Oh on a lake?". No in the streets. "What?"
People are always basing their conditions on their experience and known world view, but the present is always changing, the underlying conditions are always uncertain. I love to row on the roads, especially in the snow, I love to bicycle on the ocean. I am not joking.
Paul Wilmott has some good points on his recent blog
| Magicians And Mathematicians, how wrong many bad-quant are when it comes to probabilities. Yes all probabilities are conditional; there is no such thing as unconditional probabilities. I tried to illustrate similar (but more exotic) concept in my “Coin Flip Blow Up Article” some years back in Wilmott Magazine (also in my book Models on Models). Paul's example is much more down to earth, much more practical, here the conditions are more normal, my example was based on some hidden conditions up in a zero gravity environment. My example was similar to watching a magician that you had no clue was a magician. But then that Paul’s example is more practical is again based on uncertain conditions. If some of my friends are astronauts then may be my 'coin flip blow up' example is more practical under my conditions. Paul tend to hang out with magicians and is also some sort of magician himself. I tend to hang out with people rowing in the streets. |
Of course we never fully know the conditions or even the present, but most quants implicitly assume they do, at least in their models, and many of them even trust their models. We never know the present situation with full certainty. The present is changing continuously (or at least at every planck second depending on your probability assumptions/conditions around physics). And no object or living form can have all the information all the time. Information takes time to go from one place to another, and information is part of the present, information is energy, energy is mass, mass is energy , when information moves so also do the present. Even trying to collect information or observe something will affect the present and the future. If the magician gets the feeling some in the audience will recognize his trick, he will possibly change it into another trick in the last moment. If you want to observe properties of an electron you need to shoot something at it (other electrons, photons or whatever the physicist call these partly ‘unknown’ entities) and this will affect some properties of the electron you are observing. The more details you want to know about the present situation the more you will affect it and also the future. No this is not only at a quantum level but also in every day life, for real objects like humans. If you in the middle of a magic show suddenly run over to the magician to try to uncover his trick then you could certainly affect his trick (or his body guards). If you think a bank is quoting you a price you can arbitrage and you then get uncertain if this really is an arbitrage opportunity, then the more you dig into the situation the more likely the counterpart will figure out he/she is quoting a too good price. The more information you seek about the current situation then in general the more likely you are to affect the ‘current’ conditions. This happens in the market all the time, and then the counterpart could quickly pull their bid or offer. Well often I even tell people when they can be arbitraged, at least if they obviously simply miscalculated and gave me ridiculous wrong price in my favor. I also tell them when they try to rip me off. In general I want good long term business relationships (long term greed versus short term greed).
That all probabilities are conditional and that all conditions are uncertain, basically means there are no true probabilities. At best we can only talk about uncertain probabilities. Yes some probabilities are much more probable than others, the more information you collected the longer time series you have the better you will in general be to estimate probabilities. That is most of the time. But here also comes the danger. The more information you have, the more experience you have with standard probability calculus etc. the more likely you are to be confident or even over-confident. This is when you will do the biggest mistakes. When the conditions behind your probabilities have changed.
My friends next time I tell you I am going out to do some rowing, do not expect it to be in the streets or on water, it will be somewhere else.
Wow, so I was not the first thinking about quant finance adjustments at speeds close to the speed of light. Dr. Mark Lauer a sydney quant just made me aware of a research paper by Paul Krugeman (that at the time of Interstellar research was at Yale University):
| The Theory of Interstellar Trade, July 1978 |
"It should be noted that, while the subject of this paper is silly, the analysis actually dose make sense. This paper, then, is a serious analysis of a rediculose subject, which is of course the opposite of what is usual in economics"
Professor Paul Krugeman had an excellent point. Most ideas in mathematical finance today are on very serious subjects but often with rediculouse solutions based on a lot of unrealistic fantasy assumptions. Continuous dynamic delta hedging to argue for risk neutral valuation is just one of them (that fails completely in practice). Spacetime-finance on the other hand is extremely robust, but yes it is on a silly subject with few if any practical implications of todays only global economy (but yes practical measurable).
From the paper it looks like Professor Paul Krugeman now at Princeton University even got a grant to look into this topic, more grants should be given to such crazy topics.
While Paul Wilmott thinks it is the end of the world if we get alian visitors (see his blog) I am a great optimist and think this will be the time when we go from global-economy to a universe-economy, and yes spacetime-finance will then be of great importance.
I have not yet got time to look into his paper in detail. All I know is that I once got my invitation from a from a academic instititutions withdrawn once I mention would prefer to talk about Space-time finance. Good to see that the very best universities are a bit more open minded ;-)
So then I am not the only crazy person on this planet !!!
hemm in the 1978 paper there is a reference to a 1987 paper by same author, how is this possible???? is this paper a practical joke or is the 1987 reference simply a time-travel joke? Well Paul Krugman just told me the 1987 reference just was a time travel joke, so no time travel machine (at least not of this magnitude) yet then.
A couple of the readers of my “Option Pricing Formulas” book keep sending me e-mails about page 71-73 where I describe Phi/Rho-2. Phi is the option’s sensitivity to change in dividend yield, or foreign interest rate. The question from these naughty readers are concerning the example where they have spotted that the stock price and strike price are Fibonacci numbers, further that the result of calculating Phi is 1.6180. Phi is said to be related or connected to the Golden Ratio 1.6180. From the readers I understand this is considered a sacred or magical number. So is the example a coincident? Do the example have any meaning beside its option sensitivity?
What can I say? A good book should have more than one layer of wisdom ;-) I have to warn you, those seeking the true alchemy of derivatives will easily get lost and never get out of the labyrinth of option pricing formulas. If you not have the knowledge to enter the labyrinth you better not walk in.
Quants do not do Da Vinci Code we do Computer Code, some do VBA, some do C++ and the most Geeky ones do Pure Code ;-) Most quants understand C++ or JAVA, but few of them know ancient code.
Today I got reminded of how bad we are at understanding risk, and how we get hit when we least expect it:
Suddenly I hear what I think is an explosion just outside my door. I run out to see what it is. My neighbor had just parked her car inside her solid garage, but inside the garage she almost got hit by a car. A new BMW had just gone through her fence on back side and then almost through wall. Unlikely and completely outside most people’s probability distribution, this was also outside my probability distribution....
A tree was taking most of the hit... in the old times they built solid hedges sometimes even using trees!! at that time to protect agains cattle and wild annimals, but it also works for wild BMW's......recommended literature : Caldwell's 1870: "Treatise on Hedging"
From Preface: "His expereince has thought him that there is no one subject of such vital importance to all classes of our fellow-citizens as this subject of Hedging."
Just as true today as it was then!!! I am not sure what would have suprised Caldwell most if he could travel into the the future(that is the present): Hedging actively used for volatility swaps, or his old hedging method working well agains wild BMW's in the hedge fund capital....the world is always changing, but the main principle of hedging stays the same!