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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."
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?
Because we can't get the time off work..
It's very simple. What part of "We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach" you didn't understand?
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.
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
I'm an analyst for a large financial firm, and this is actually old news for us soul-sellers. There is no good options pricing model; they all have problems.
These articles should help clear things up:
http://en.wikipedia.org/wiki/Binomial_options_pricing_model
http://en.wikipedia.org/wiki/Black-Scholes
http://en.wikipedia.org/wiki/Monte_Carlo_option_model
To the Wikipedia-mobile, Geek Wonder!
It's very simple. What part of "We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach" you didn't understand?
The vanilla part, of course. After all, why should it matter if the options come in vanilla or chocolate flavour? :-)
The Tao of math: The numbers you can count are not the real numbers.
Isn't it just a bet on the variance of the underlying stock? Skimming over those models, they look like they're really all just different ways of mutating your choice of initial assumption about the distribution of possible futures.
Because we have a perfectly good constitution that doesn't need to be "fundamentally transformed". We believe in the rule of law, not men, so the only "revolution" that needs to happen is to kick the lawbreakers out of our government-- and imprison them, if necessary.
Gamingmuseum.com: Give your 3D accelerator a rest.
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.
>
I come from a country which has experienced a revolution in my lifetime.
Why can't you?
We can. We choose not to.
If your question is, "why don't you?" Then that is because I don't feel like a revolution will solve the fact that wall street is using substandard formulas (that is what we are talking about right?) and would probably cause more problems for my sound long-term investments than any pockets of casino capitalism do.
This may seem like news to you, but not all of us hate Wall Street. Some of us positively support it and what it represents (shocking, I know).
And some of us even make use of it and are better off because of it.
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.
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.