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Gosper's Algorithm Meets Wall Street Formulas
peter.hill.1980 writes "Wall Street's money making formulas need to be as explicit as possible for efficiency purposes. An old, existing and famous formula — binomial options pricing formula — has now been scrutinized for theoretical optimality in a forthcoming paper by Evangelos Georgiadis of MIT using Gosper's Algorithm, proving that no general explicit or closed form expression exists for pricing."
Iz deoznt understandz dis
"A person is smart. People are dumb, panicky dangerous animals and you know it." - K
Why do Americans across the country not simply not occupy Wall Street?
Why have you been so effectively programmed to accept the shit you're fed?
Not a statement against sound long-term investment, but against casino capitalism and cronyism.
I come from a country which has experienced a revolution in my lifetime.
Why can't you?
I suppose instead of interesting stuff like this that not everyone necessarily understands, /. should stick to opinion blogs about the color of Steve Ballmer's socks.
I don't really understand this... does this mean that it is not determinable whether an option pricing formula for European puts/calls is optimal or what??
BUSTED!
Georgiadis (NOT Georgiaids)
as the bid/ask spread generally exceeds any theoretical differences between models.
The basic form of the algorithm (according to *AA groups) is as such: $Max_Payable_Price times ($Total_World_Population - $Steenking_Pirates). *AA's obviously want to minimize the $Steenking_Pirates, especially the ones who simply don't listen to their music in the first place.
Many lawmakers agree with this, with the agreement being proportional to the money they receive from the *AA's.
And yes, I know that people who don't listen to music shouldn't need to pay, but I dare you to tell the RIAA that. It's even worse when these groups refuse to sell a (legal) product for any amount of money and then sue you for buying it from someone who is willing to sell it to you.
just wow
And what does this have to do with option pricing? It just proves that there is no closed form. From the quick little research I did on closed forms, all this means is that you can't use limits or integrals, which are used as solutions for a slew of real world problems.
ahh see there Gosper was MIT so is John Cox (creator of binomial options pricing model). interesting how the flow of ideas concentrates and propagates ... MIT^cubed
It seems, after reading through the paper (to the extent my non-MIT mind understood things) that this is based upon a pricing model of European options. European options can only be exercise on the expiry date, American options can be exercised any time before that date.
no algorithm exists for stupidity either
This is the abstract used ( not really) to get teh funding grant for this research.
Two fundamentally different but complementary transition metal catalyzed chemo-, regio-,diastereo-, enantio-, and grantproposalo-selective approaches to the synthesis of a library of biologically significant nano- and pico-molecules will be presented with the focus on reaction mechanism and egocentric effects. The role of the nature of the metal, ligand, solvent, temperature, time, microwave, nanowave, picowave, ultrasound, hypersound, moon phase, and weather in this catalytic, sustainable, cost-effective, and eco-friendly technology will be discussed in detail.
quis custodiet ipsos custodes
As if we needed fancy mathematics to tell us that the formulas used by Wall Street traders don't work. Let me offer you Exhibit A.
When pricing options the bionomial way, one creates a sort of decision tree for movements the underlying value makes. (scroll down on http://software.intel.com/en-us/articles/high-performance-computing-with-binomial-option-pricing-part-1/ to see such a tree).
This paper seems to prove that there is no easy formula short cut for the tree: if one wants to know the answer, one really needs to build the entire tree.
What it means is that they've finally proven that all these quants coming out of school making six digits really don't know what they're doing and the next time their crappy options pricing models break down and cause a financial crisis, we can all point and say "I told you so."
should be called the Bachelier-Thorp formula ( at least according to Taleb).
( Bachelier used Brownian motion in his work on options before Einstein applied it to physics) .
Yours In Miami,
Kilgore Trout
OK, so there is no exact solution to the formula. Do you need one? Or will a Monte Carlo simulation be good enough, the way it is for (say) the physicists building nuclear bombs or the engineers designing airplanes?
Closed-form solutions are nice for proving things with arbitrary precision, but they're often not necessary in the real world, where a few decimal places often suffice.
Wow, I am surprised.
The binomial model is common in textbooks because it's intuitively appealing, but if you only apply it to basic European (exercisable at expiry) options then there really are better ways of getting a closed form solution i.e. the Black-Scholes (or Bachelier-Thorp ....) formula.
If you want half decent pricing methods for more general cases then you'll end up with Finite difference or Monte-Carlo methods depending on dimensionality, at which point you've already given up on a closed form solution.
One of the reasons that TFA is so unintelligible is it's an academic treatment of half of the theory of a non-problem. (and as others have already pointed out - it has nothing to say about how the finance industry operates).
as "Devil takes the hindmost" (by Edward Chancellor) points out, many traders will be offended by your vulgar terminolgoy.
they are 'hedging', they are 'creating efficiencies', they are 'earning', they are absolutey not, in no way, gambling.
i hate to tell you but 'wall street' is not even home to that many 'wall street firms'. it is mostly in cyberspace now.
even the big banks have moved up town. but besides that.
the electronic trading has taken over. hedge funds are built in people's spare rooms, they trade in their underwear.
the center of AIG's credit default swap business was in London at AIG Financial Products division. Not in the US, not in America.
the Chinese banks owned massive amounts of Fannie and Freddie debt, and were leaning on the Bush adminsitration not to default (even though the Russian govt tried to team up with them and crash us even harder). More info on this in 'on the brink' buy Hank Paulson.
One of the biggest customers of CDO tranches was Germany. but it was spread over the world. Norway, Australia, etc.
And Deutschebank, one of the biggest 'wall street banks', is not headquartered in the US. Nor is Credit Suisse, both of these hugely involved in the synthetic CDO market. In "the big short" one of the major characters works for deutschebank.
That is the whole point of the elimination of glass-steagall in the first place, the Europeans never had a law separating commercial and investment banking like the US did. Thus the US banks claimed it was hard for them to compete against their gargantuan European rivals.
When Lehman and Bear Stearns were both in crisis, they were both reaching out to asian banks. Morgan Stanley, if not for a Japanese bank, would quite probably not exist today. You can read about all this in The Sellout, Too Big to Fail, On the Brink, Devils Casino, House of Cards, etc etc etc.
The most pertinent to the topic is "The End of Wall Street" by Roger Lowenstein.
All of the classic activity thought of as 'wall street activity' doesnt exist on wall street. There are no major american banks that are classified as Investment Banks anymore.
Morgan Stanley - now regulated as a holding company (ie. regulated by the Fed)
Goldman Sachs - same as Morgan
Merrill Lynch - bought by Bank of America, which is regulated by the Fed
Bear Stearns - bought by JP Morgan Chase, regulated by the Fed
Lehman Brothers - bankrupt
There are no American 'investment banks' operating on an 'investment bank model'. the functions they performed in the economy are now performed by other entities, either hedge funds, private equity firms, funds of funds, venture capitalists....
This doesnt even address what this means for European banks like Credit Suisse, Societe Generale, Deutsche Bank, Barclays, etc, who work under European regulation, not US regulation. Are those now going to take over 'investment banking' business in the US? Then there are the Japanese banks, and the new Chinese banks, which are an absolutely fascinating entity in that the communist party controls them, and people are believing the numbers coming out of them pretty uncritically.
Wall Street is everywhere. Wall street is in your 401k. It is in your iphone. It is in your mortgage. It is in your credit card. It is in your student loan. It is in every last piece of debt you will ever have. It has been sliced up, and resold, and someone took a cut. That someone could be anywhere on the planet.
Wall Street is us.
there is plenty of evidence that a large amount of the theory behind modern academic economics is based on payola and a religious belief, not on empiricism or on any sort of scientific rigor
The naive CRR (Cox, Ross, Rubinstein) method for pricing options is O(n^2) where n is the number of levels in a recombinant binomial pricing lattice. That is, a lattice like a binary tree, but where you have cross links connecting nodes. The naive approach requires visiting each one of these nodes and hence O(n^2) and the error of the produced option goes down only proportional to the node spacing. For at least 15 years this problem has been converted to "linear time" (really the important relation is between the price error and the CPU time) by means of a variety of extrapolation methods (this began with Richardson extrapolation) using evaluation with two trees to get a much smaller error. There are in fact numerical methods that for special options can do slightly better than this. Broadie 1996 is one reference. While pretty fast and very easy to understand, there are yet faster methods using adaptive mesh crank-nicolson PDE solvers that do a bit better. Just a couple of years ago, Dai, et al. published a paper showing how to get linear time an entirely different approach involving combinatorial sums. This may have improved performance bounds for some exotic options, but did NOT do much for improving real-world implemented algorithmic performance of pricing the European and American options that are so commonly traded on exchanges, in the US and worldwide. So, at least for the most important class of options Dai et al was kind of a snoozer. The paper referenced in the summary above is entirely a follow-up paper to Dai, et al 2008. This new paper merely shows that there is no "short cut" in evaluating the relevant sums with hypergeometric functions, a kind of special function common in mathematical physics. So, in short, all this says is that the already "non fastest method" cannot be made faster by one numerical methods approach. It is certainly deserving of publication and dissemination, but changes the world not at all.
This has not, however, stopped their earnings from pushing back the boundaries of pure hypermathematics, and their chief research accountant has recently been appointed Professor of Neomathematics at the University of Maximegalon, in recognition of both his General and his Special Theories of Disaster Area Tax returns, in which he proves that the whole fabric of the space-time continuum is not merely curved, it is in fact totally bent.
It absolutely is gambling and any investor who denies this is either dishonest or not very well informed. I infer from your sarcastic quote marks that I'll enjoy Edward Chancellor's book -- sometime after I enjoy Taleb's, and Reich's, and ...
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
The subject is a rigorous mathematical proof that what we're told about capitalism being efficient is inherently less generally true than the sweeping, absolute terms that especially conservatives and libertarians like to claim. Direct implications of this proof include: de-regulation legislation like the Credit Futures Modernization Act & Gramm-Leach-Bliley, whose "value" was alleged to have been in facilitating more rapid exchange of capital and thereby greater "efficiency," now provably can only deliver more opportunities to gamble. Events since 15 September 2008 already constituted strong circumstantial evidence, but this is absolute proof. That's a rigorous, mathematical proof mind you. What that means is indeed absolute proof. Unless an error is found in the math, this means everything we've been told about the "benefits" that Wall Street offers society, for at least a generation, is hogwash. AC's commentary on the implications is not offtopic. You just dislike the implications. Tough shit.
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
multifaceted wisdom
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
I'm good for a laugh. What great thing does today's Wall Street represent to you?
I'd like to know also.
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
It's criminal conspiracy.
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
This is probably one of the stupidest topics for a paper I've seen in recent memory. Nobody, NOBODY, uses binomial lattices to price European options. Black-Scholes is the model used to price European options--it's so ubiquitous that option prices are often quoted as the Black-Scholes volatility rather than the dollar price ("I'll sell at 30 vols" rather than "I'll sell at $5/contract"). At the very least they should have examined American options or Asian options--something that doesn't have an explicit formula under the usual continuous-time model.
Moreover, this result is completely trivial given today's technology. An undergrad, if not a high school student, with an implementation of Gosper's algorithm could have easily done this. Why someone even thought of submitting this to /. is a facepalm for me.
in Devil Take the Hindmost , by Chancellor, he deals specifically with the question and lays out the definitions proferred by students of the question in the past.
speculation, gambling, hedging, and business activity are four distinct endeavors. some bleed into the others but there are definite features of each that the other lacks.
I recently had a master's course in derivatives, including binomial option pricing, and I have no idea what's going on here.
pretty ...
The difference, and the reason your analogy is shit, is that aeronautical engineers don't claim to know the existence and smoothness of the Navier-Stokes equations in R3. If you ask them, they're honest about which of their equations are just assumptions and why they believe they're valid assumptions. What economists, especially those employed by corporate lobbying firms, have been claiming to anybody with a microphone and camera or a steno pad for decades, is that more trading is always good because, they claim, market actors rationally pursue profit while having "perfect information" about the things they're trading. This paper does prove the latter assumption invalid for these classes of speculative trade. So please, make some more sweeping generalizations about what you stupidly assume that I don't know, jackass.
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
The difference, and the reason your analogy is shit, is that aeronautical engineers don't claim to know the existence and smoothness of solutions to the Navier-Stokes equations in R3.
There, fixed that for myself.
"I can't imagine how things could get any worse!" (some guy) "That could just be failure of imaginatioÂn on your p
It is when you pull it off as masterfully as Goldman Sachs did