Beta
×

Welcome to the Slashdot Beta site -- learn more here. Use the link in the footer or click here to return to the Classic version of Slashdot.

Thank you!

Before you choose to head back to the Classic look of the site, we'd appreciate it if you share your thoughts on the Beta; your feedback is what drives our ongoing development.

Beta is different and we value you taking the time to try it out. Please take a look at the changes we've made in Beta and  learn more about it. Thanks for reading, and for making the site better!

Gosper's Algorithm Meets Wall Street Formulas

Unknown Lamer posted more than 3 years ago | from the hypergeometric-overlords dept.

Math 124

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."

Sorry! There are no comments related to the filter you selected.

Hurh? (1)

ArhcAngel (247594) | more than 3 years ago | (#35360778)

Iz deoznt understandz dis

Re:Hurh? (1)

hedwards (940851) | more than 3 years ago | (#35360818)

Indeed, I realize that this is /., and that /. doesn't have any editors, but this is pretty ridiculous. At least link to something that has some information if you can't be arsed to create an informative summary.

Re:Hurh? (0, Troll)

Anonymous Coward | more than 3 years ago | (#35361088)

Indeed, I realize that this is /., and that /. doesn't have any editors, but this is pretty ridiculous. At least link to something that has some information if you can't be arsed to create an informative summary.

i resent that remark. slashdot has the very best editor niggers that a watermelon and a bucket of fried chicken can buy.

to prove it they'll make haste to use their infinite mod points to mod this down to -1 since it says the word "nigger" and that triggers instant OH NO, ALERT ALERT UNAPPROVED WORD I FEEL SO OFFENDED NOW ... but they won't fix the fucking summary. they gots priorities yo.

Re:Hurh? (5, Funny)

mangu (126918) | more than 3 years ago | (#35360972)

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?

Re:Hurh? (2)

maxwell demon (590494) | more than 3 years ago | (#35361424)

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? :-)

Re:Hurh? (1, Funny)

Burnhard (1031106) | more than 3 years ago | (#35362312)

Why is this modded "informative"? It should have been modded funny.

Re:Hurh? (1)

c0lo (1497653) | more than 3 years ago | (#35362982)

Why is this modded "informative"? It should have been modded funny.

For the fun of it.

Re:Hurh? (1)

locallyunscene (1000523) | more than 3 years ago | (#35363074)

The part where a lost all my money.

Aaaand it's gone.

Re:Hurh? (0)

Anonymous Coward | more than 3 years ago | (#35363640)

tl;dr even an oversimplified model of human behaviour isn't simple enough.

Lol, economists. Always trying to model the worker as a number and surprised that, despite all his work, the world still ends up in the shit every 20-30 years.

Re:Hurh? (0)

Anonymous Coward | more than 3 years ago | (#35364642)

"vanilla European call "

Re:Hurh? (4, Informative)

Anonymous Coward | more than 3 years ago | (#35361184)

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 [wikipedia.org]
http://en.wikipedia.org/wiki/Black-Scholes [wikipedia.org]
http://en.wikipedia.org/wiki/Monte_Carlo_option_model [wikipedia.org]

Re:Hurh? (3, Insightful)

Fractal Dice (696349) | more than 3 years ago | (#35361426)

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.

how dare you (3, Interesting)

decora (1710862) | more than 3 years ago | (#35362456)

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.

Probability Theory began with games of chance. (1)

ReedYoung (1282222) | more than 3 years ago | (#35363652)

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 ...

Re:Probability Theory began with games of chance. (0)

khallow (566160) | more than 3 years ago | (#35364736)

The refined financial term is "speculation". It only becomes "gambling" in the business sense when you crater something.

While I sense a great deal of sarcasm in this thread, it is worth noting that speculation actually can result in positive return over long periods of time. Some people are very good trader/gamblers and their talents shouldn't be denied. But the problem comes when you have high leverage amplifying all the risks of the market and the business.

High leverage where one borrows staggering amounts of money (something like 50 borrowed dollars to 1 dollar of assets was common in the recent real estate crash) will guarantee a crash even for very stable investments.

And if you're speculating at the same time you're applying ridiculous leverage? Well that's something like juggling live hand grenades while wheeling your unicycle on a greased tightrope over a canyon with no net. Something bad will happen to you sooner or later.

Re:Probability Theory began with games of chance. (1)

ReedYoung (1282222) | more than 3 years ago | (#35365406)

While I sense a great deal of sarcasm in this thread, it is worth noting that speculation actually can result in positive return over long periods of time. Some people are very good trader/gamblers and their talents shouldn't be denied. But the problem comes when you have high leverage amplifying all the risks of the market and the business.

Totally agree. I almost said the same thing, but just wanted to be sure not to say too much. I tend to go on a bit, you see. :-)

But since somebody is interested, I'll say that a very important distinction is knowing the odds and playing them smartly, versus guessing the odds skillfully/luckily. Over time, luck always runs out eventually. So says the Strong Law of Large Numbers.

High leverage where one borrows staggering amounts of money (something like 50 borrowed dollars to 1 dollar of assets was common in the recent real estate crash) will guarantee a crash even for very stable investments.

In other words, a "black swan" is sure to come by, eventually. So only fools construct systems in which one "black swan" will ruin everything, just because "black swans" are estimated to be rare, within the parameters of assumptions that are necessarily incomplete, flawed and non-absolute anyway.

And if you're speculating at the same time you're applying ridiculous leverage? Well that's something like juggling live hand grenades while wheeling your unicycle on a greased tightrope over a canyon with no net. Something bad will happen to you sooner or later.

Or, in the case of Wall Street, "... on a greased tightrope between skyscrapers, over crowded streets with no net. Sooner or later, something bad will happen to you, the reckless idiot juggling live hand grenades while riding a unicycle on a greased tightrope who deserves to die messy, and something bad will happen to a lot of innocent bystanders who did not choose to take such moronic risks.

The refined financial term is "speculation". It only becomes "gambling" in the business sense when you crater something.

I'm sure it is. Somehow, I just can't seem to care what gamblers who off-shored the vast majority of my country's entire industrial base then devalued what was left with their incompetent and corrupt gambling habits, prefer that I call their activities. In a casino, whether you win or lose, you're a gambler. So I won't acknowledge that distinction for the same type of behavior, just because it takes place in a different setting, a setting in which they keep any winnings, and pass on all losses to the working people of the country, by the way. Win or lose, it's gambling. And now we know, mathematically, gambling is literally the correct term; it's only roughly-informed risk-taking, like playing blackjack with a deck of approximately 52 cards, +/- ... how many? They don't know and I won't go along with nomenclature that has no purpose but to forge the impression that their risk-taking is more informed than it is.

When they give back GM workers' pensions, I'll consider giving a fuck what Wall Street gamblers wish me to call them and their gambling.

Re:Hurh? (1)

ReedYoung (1282222) | more than 3 years ago | (#35363572)

But was there a mathematical proof? Or just 'Street common wisdom & anecdote, that no sure-fire formula exists?

The summary: "... proving that no general explicit or closed form expression exists for pricing."

There is something new here. I get your point that Wall Street will not change its ways because you and every other trader have already been assuming what this paper proves, and I don't doubt what you said one bit, but for the rest of us this is significant because formal, incontrovertible mathematical proof that stock trading is to a degree inherently irrational absolutely puts the lie to the anti-regulation, libertardian free market BS spouted by "think" tank "experts" in "mainstream" corporate news and commentary. Whether this fact will propagate to general common wisdom is another matter, but this proof is culturally and politically significant even if nobody notices that it is.

Re:Hurh? (1)

sabre86 (730704) | more than 3 years ago | (#35364862)

inherently irrational

I hope that's a really clever pun. Says Wolfram Mathworld on Gosper's algorithm

The algorithm treats sums whose successive terms have ratios which are rational functions.

Re:Hurh? (1)

ReedYoung (1282222) | more than 3 years ago | (#35365416)

No pun intended. Any "funny" mods for that pun are rightfully yours.

Re:Hurh? (4, Informative)

emurphy42 (631808) | more than 3 years ago | (#35361228)

To the Wikipedia-mobile, Geek Wonder!

  • Option [wikipedia.org] , e.g. "I pay you $100 and you agree to (sell to me / buy from me) 1,000 shares of XYZ at a locked-in price of $50 apiece whenever I decide to exercise my option" (I may decide not to exercise it at all, and I may have a time limit)
  • Binomial options pricing model [wikipedia.org] , a formula for how valuable an option is in practice
  • Closed-form expression [wikipedia.org] , pertaining to a method that gets values out of a formula without resorting to brute-force approximation or other such PITA methods
  • Gosper's algorithm [wikipedia.org] , pertaining to proving that there ain't no such method for this model

Re:Hurh? (0)

DarkAxi0m (928088) | more than 3 years ago | (#35363874)

  • To [wikipedia.org] , a Grammatical particle
  • the [wikipedia.org] , the definite article
  • Wikipedia [wikipedia.org] , WAIT! STOP you can't view the Wikipedia page on Wikipedia,
    you will implode the internet,
    and then the universe!!!!
    DON'T CLICK THAT LINK!!

be an American (-1, Offtopic)

Anonymous Coward | more than 3 years ago | (#35360822)

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?

Re:be an American (4, Insightful)

spiffmastercow (1001386) | more than 3 years ago | (#35360876)

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..

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35361086)

The Egyptian army would have been happy to support you on your day off. Do you feel your own army won't?

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35361514)

Because we can't get the time off work..

Wrong. It's because our bread come pre-sliced. That prevents you from tying an entire loaf to your head, and single slices are simply not effective protective headgear [knowyourmeme.com] .

Re:be an American (1)

rcamans (252182) | more than 3 years ago | (#35362222)

We can't get the PAID time off work...

Re:be an American (-1)

Anonymous Coward | more than 3 years ago | (#35361280)

You are a fucking idiot.

Re:be an American (0)

kronosopher (1531873) | more than 3 years ago | (#35361436)

Why can't you?

Typical Americans are more interested in football than the downward spiral of society. Not only that but the establishment psychologically condi.. SQUIRREL!

Re:be an American (2)

operagost (62405) | more than 3 years ago | (#35361474)

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.

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35361898)

Because we have a perfectly good constitution that doesn't need to be "fundamentally transformed".

I have a perfectly good knife. It just seems to have stopped cutting.

We believe in the rule of law, not men,

Every country's patriots think so. You have rule of law. But with so many laws that anyone can be branded a criminal. Oh, and unequal accessibility to the law. Which is another way of achieving rule of men.

so the only "revolution" that needs to happen is to kick the lawbreakers out of our government-- and imprison them, if necessary.

Every revolution involves
(i) a subset of people (33%)
(ii) declaring a set of principles that they believe should always have applied; and
(iii) observing that they don't currently apply thanks to
(iv) the corruption of the power elite, therefore
(v) declaring that this elite is unpatriotic, so
(vi) declaring that the elite must be overthrown.

If you read just (i) and (vi), you'll understand that revolution is just putting the country into maintenance mode for a while. Everyone does it out of love for his country and out of love for some principles that he feels apply to it (even if they never really have). Don't think you're any more special for believing this too.

Mod up (1)

ReedYoung (1282222) | more than 3 years ago | (#35363782)

multifaceted wisdom

Re:be an American (2)

psithurism (1642461) | more than 3 years ago | (#35361694)

>

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.

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35361716)

Do you have any idea how that would affect my 401k?

Re:be an American (2)

metlin (258108) | more than 3 years ago | (#35361750)

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).

Re:be an American (2)

jgtg32a (1173373) | more than 3 years ago | (#35361778)

And some of us even make use of it and are better off because of it.

Re:be an American (1)

garyebickford (222422) | more than 3 years ago | (#35364026)

I'm up 250% since the $140 oil spot (2008?)

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35362160)

But you aren't a angst-ridden freshman majoring in Sociology, and therefore don't know what you're talking about.

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35362326)

I'm the OP AC. Mathematics postgrad. Interest in economics. In short, no, I'm as far from "sociology freshman" as you can get. My argument isn't some pathetic slashdottian binary "either communism or Wall Street". There is so much intelligence which went into building capitalism up to the beginning of the 20th century and which has been all but wiped out from it in the century since

The downward spiral has been particularly insidious since Reagan/Thatcher, the most enduring anti-capitalism capitalists the West has had the misfortune to have been hoodwinked by.

If you think it's good because it made you rich, you're just another Mubarak whose family's time hasn't come yet.

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35362234)

I'm good for a laugh. What great thing does today's Wall Street represent to you?

Seconded. (1)

ReedYoung (1282222) | more than 3 years ago | (#35363790)

I'm good for a laugh. What great thing does today's Wall Street represent to you?

I'd like to know also.

Re:be an American (1)

Eightbitgnosis (1571875) | more than 3 years ago | (#35361762)

Simply? What the hell is simple about attempting to remake the economic capital of the entire planet?

Re:be an American (1)

khallow (566160) | more than 3 years ago | (#35361890)

I come from a country which has experienced a revolution in my lifetime.

Why can't you?

We had three recent ones in 2010, 2008 and 2006. I think you just don't know what a revolution looks like.

Re:be an American (0)

Anonymous Coward | more than 3 years ago | (#35361984)

We will when the time is right.

wall street doesnt exist anymore (1)

decora (1710862) | more than 3 years ago | (#35362570)

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.

Re:be an American (1)

Princeofcups (150855) | more than 3 years ago | (#35362852)

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?

Break and circuses. The people are well fed, well entertained, and generally very lazy. Half of the country is kept in a constant state of paranoia, hatred of gays/Muslims/liberals, and worship of the moneyed rich. They're the better armed half also. The counter revolution would nearly impossible to oppose.

Re:be an American (1)

sjames (1099) | more than 3 years ago | (#35363068)

It's a bit like superheated water. There's a lot of anger against banks, Wall street, and politics in general, just waiting for a nucleation point. Sort of like when you heat a cup of tea in the microwave and all seems well, then you add sugar and it explodes in a cloud of steam.

AC is not offtopic (1)

ReedYoung (1282222) | more than 3 years ago | (#35363752)

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.

Complaining (0)

Anonymous Coward | more than 3 years ago | (#35360846)

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.

Re:Complaining (1)

ReedYoung (1282222) | more than 3 years ago | (#35365494)

Okay, then. In my opinion, the color of Steve Ballmer's socks is responsible for Scott Walker, Koch Industries, the explosion of BP's Maconda Well, the disinformation from "Curveball" that the Junior Bush administration chose to use as the pretext for Operation Iraqi Liberation, the increasing rate of unemployment in the United States as well as all the very-long-term-unemployed who no longer qualify to even be included in the "official" unemployment statistics, and, oh yeah, exceptions to H1-B law obtained by Microsoft under false pretenses. [arstechnica.com] I realize some of those connections are a bit tenuous, but Bill Gates certainly didn't use his best judgment when he lied in an op-ed in the Washington Post, in an interview with David Broder, and every time he testified to Congress that the "talent" Microsoft seeks just isn't available in the United States. Maybe Steve Ballmer's socks were playing tricks on his mind. Or maybe he's just a douchebag.

What? (1)

linux_geek_germany (1079711) | more than 3 years ago | (#35360886)

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! (0)

Anonymous Coward | more than 3 years ago | (#35360894)

BUSTED!

Re:BUSTED! (0)

Anonymous Coward | more than 3 years ago | (#35361068)

I reject your reality and substitute my own!

Georgiadis (NOT Georgiaids) (1)

Anonymous Coward | more than 3 years ago | (#35360900)

Georgiadis (NOT Georgiaids)

Doesn't really matter (1)

Lawrence_Bird (67278) | more than 3 years ago | (#35360912)

as the bid/ask spread generally exceeds any theoretical differences between models.

Basic Form: (0)

Even on Slashdot FOE (1870208) | more than 3 years ago | (#35360926)

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.

Re:Basic Form: (0)

Anonymous Coward | more than 3 years ago | (#35361212)

I have no idea what this has to do with the article at hand, but I agree with the interpretation.

wow (0)

Anonymous Coward | more than 3 years ago | (#35360942)

just wow

And this means? (1)

bpeikes (596073) | more than 3 years ago | (#35360954)

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.

Re:And this means? (0)

Anonymous Coward | more than 3 years ago | (#35361020)

, all this means is that you can't use limits or integrals, which are used as solutions for a slew of real world problems

LOL.

I'm going to forward this to the quants in the place where I work.

Re:And this means? (1)

ArhcAngel (247594) | more than 3 years ago | (#35361626)

We fired all our quants and got a pretty girl to create power point presentations and display them in meetings every morning. It seems to be just as effective and a damn site more enjoyable.

Re:And this means? (0)

Anonymous Coward | more than 3 years ago | (#35361738)

Since you can't use limits or integrals, maybe this means Ito_calculus [bit.ly] is something that can't be used for options pricing? It is a branch of mathematics in the financial world. (a bit.ly link had to be used due to broken character filtering...)

MIT^3 (1)

Anonymous Coward | more than 3 years ago | (#35361008)

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

European not American option pricing (3, Informative)

milgram (104453) | more than 3 years ago | (#35361024)

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 [slashdot.org] . European options can only be exercise on the expiry date, American options can be exercised any time before that date.

Re:European not American option pricing (0)

Anonymous Coward | more than 3 years ago | (#35361264)

see also wikipeadia entry ; http://en.wikipedia.org/wiki/Binomial_options_pricing_model

The binomial options pricing model has a lower bound on complexity that rules out a closed-form solution.

Re:European not American option pricing (2)

Fnkmaster (89084) | more than 3 years ago | (#35361882)

More specifically, the paper proves that there is no closed form expression for the *binomial* options pricing model on a European put or call.

There's a closed form for European options pricing, under certain assumptions, which is of course the Black Scholes formula. The paper notes this obvious fact in footnote 7.

The binomial model is generally more flexible, and allows the tweaking of assumptions (dividend payments, etc.). As a result, it's used in practice to value certain types of options (exotics, stuff with crunky payout schedules, barrier options, etc.).

I believe the same applies to American options, though I have no clue off the top of my head if it's been proven or not - i.e. there's no known closed form expression for the arbitrary binomial sum in the binomial pricing model. Though I do recall some of what I recall as approximation formulas from my Advanced Derivatives class. But that was quite a few years back so my memory could be fuzzy.

I'd say this is a cool proof, but it's not like people were sitting around wondering "gee, is there a closed form expression for this?" because they are either using simple approximations or programs that run a full binomial simulation to the desired degree of accuracy in such exquisitely fast periods of time that it's probably irrelevant.

And the existance or lack thereof of a closed form expression doesn't really have any deeper theoretical impact that I can think of. But still a cool result.

Re:European not American option pricing (2)

plopez (54068) | more than 3 years ago | (#35363024)

"And the existence or lack thereof of a closed form expression"

I am a modelier (a fancy pants way of "I configure and run models") though not in Economics. This has *huge* implications for the practical application of models. Now, what no closed form solution means is that there may be a number of different paths that a solution can be achieved. You can converge from a number of different directions, and be "right for the wrong reasons". "Great!", you say, "if I am wrong on one of my parameters, this means it will still converge!". Ummmm.... the problem with that is with no closed form solution you cannot *prove* it will converge to an global optimum for a given set of parameters. You have to seek them out.

Also in a non-linear system, which I assume Economic and Market Models are, you have a great amount of sensitivity to initial conditions and also parameter sensitivity. If you have run into the non-uniqueness problem then a slight shift in parameters or initial conditions can send you spinning off into "never never" land. The model may not be robust. Even worse, if you do sensitivity analysis, like a good modelier should, you may converge to the wrong optimum repeatedly from the wrong parameter set or initial conditions. For that reason you actually want sensitive vs insensitive parameters. Sensitive parameters actually give you more information.

What scares me is so many models are blindly followed. The attitude is "I have a model and therefore a number, and therefore a predictor of reality." If you do not understand the limitations of the model you will be in for a shock one day. Also you should understand the processes which drive the system, which in Economics is psychological (both in terms of crowd mentality and gov't policy) and environmental, e.g. weather patterns killing crops, cold spells decreasing or increasing demand for heating fuel, droughts etc.

I will forgo a discussion on instrumentation noise, instrumentation calibration, stochastic models, theoretical computational error, and machine precision and their potential impacts on a model.

A note on nomenclature, when you wrote "to the desired degree of accuracy" you probably meant "to the desired degree of precision". You can be accurate (which is hard to prove) or precise or both or neither. Accuracy is "Am I close to reality? Am I getting a real result?", precision is how small is my measurement scatter. You can be very precise but not accurate, and vice versa.

Re:European not American option pricing (1)

impossiblefork (978205) | more than 3 years ago | (#35363112)

Although I've only looked at the paper briefly I think that what it proves is that there is no closed-form expression for the partial sums in the Cox-Ross-Rubenstein model. Such a closed form expression would be neat, but ultimately one only cares about the limit, where one has, as you write, the Black-Scholes formula.

I don't work with this, so this might be entirely academic- but isn't convergence in the binomial model extremely slow for barrier options?

Also, there is a nice explicit formula for all standard types (down-and-out, out-and-in, etc.) on any payoff function in Björk's book- and I think that it can be "easily" modified to support fixed continuous dividends.

Re:European not American option pricing (0)

Anonymous Coward | more than 3 years ago | (#35363242)

having read through the paper I'm not sure I see the utility of this paper beyond the getting a paper published.

Unless I missed something and I only skimmed it, they are essentially arguing there are no closed forms for the option pricing formula period, but they illustrate from the binomial tree method that no closed for hypergeometric formulas can be generated. They discount the Black-Scholes-Merton pricing formula as a closed form solution because it is based upon functions which are themselves defined as integrals.

Now forgive me if I misinterpreted what they were trying to do but it was probably obvious a priori. The Black Scholes Merton pricing formula for a European call is expressed in terms of cumulative normal distribution functions, which is the integral of the normal distribution. It is already a VERY well know result that the indefinite integral of the normal distribution CANNOT be expressed using elementary functions - i.e. polynomials - and thus it shouldn't come as any surprise that the 'closed form' solution obtained under a continuous time assumption cannot be expressed in terms of a finite sum of elementary functions by starting out in discrete time.

Regarding the American call option, the solution (IIRC) is the same as the European call option as it is never optimal to exercise an American call option prior to expiry; the same is not true for the American put, which cannot be solved analytically and for which there are regions where the put is optimal to exercise prior to expiry. This of course all assumes the Black-Scholes assumptions, which are in varying degrees completely invalid. markets are not perfectly frictionless, perfectly liquid, etc.

Re:European not American option pricing (2)

tlhIngan (30335) | more than 3 years ago | (#35362212)

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.

I'm not sure I follow. An "American option" as you call it has two dates - one is the vesting date (the first day the option may be exercised) and an expiry date (the date the option will no longer be valid). Sometimes the vesting date can be the same as the option purchase date (i.e., exercised immediately), othertimes, it can be expiry date, or anywhere in-between.

Are you saying European options only have a vesting date, and may be exercised at any time thereafter?

Re:European not American option pricing (0)

Anonymous Coward | more than 3 years ago | (#35362436)

An option with a vesting date and no expiry is a type of American option -- though typically it is distinguished as a perpetual American option, or just a perpetual option. A European option is one for which vesting and expiry happen at the same time -- ie, you can only exercise it at one point in time (read: one day).

Re:European not American option pricing (1)

mmontour (2208) | more than 3 years ago | (#35363334)

I'm not sure I follow. An "American option" as you call it has two dates - one is the vesting date (the first day the option may be exercised) and an expiry date (the date the option will no longer be valid).

It sounds like you are describing the options that are given out as an employment benefit. There is a different kind, traded on an exchange just like stocks are.

If a particular stock 'foo' is trading at $60 today but you think it is going to go up in the future, you can buy a "June $65 call" for some small amount of money. That option then allows you to buy a share of foo for $65 any time between the purchase date and the June expiration date (American style), regardless of what the stock price happens to be at that time. Obviously you would only exercise it when the stock price was higher than $65, since otherwise it would be cheaper to buy the share itself than to exercise the option.

You can also sell the option to someone else instead of exercising it. If 'foo' was trading at $75 in mid-May then your option would be worth somewhat more than $10 at that time. Figuring out how much more than $10 it's worth is what this article is about.

Re:European not American option pricing (0)

Anonymous Coward | more than 3 years ago | (#35363384)

American = exercise Anytime after they begin trading. i.e. vesting date is the date of creation
European = exercise only at Expiration. i.e. vesting date is the expiration date

Re:European not American option pricing (1)

Dast (10275) | more than 3 years ago | (#35363294)

Ah, shoot. I forgot they trade options on the opposite side of the street than we do. Drats.

!algorithm (1)

Anonymous Coward | more than 3 years ago | (#35361038)

no algorithm exists for stupidity either

abstract text (4, Funny)

PrinceAshitaka (562972) | more than 3 years ago | (#35361172)

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.

Re:abstract text (0)

Anonymous Coward | more than 3 years ago | (#35361550)

That actually makes far more sense than the summary. You need to through in a couple of more marketing and math related buzzwords.

Re:abstract text (0)

Anonymous Coward | more than 3 years ago | (#35364312)

I don't get it. The joke is you're too dumb to understand the text?

Pronoun modifier verb pronoun. Article noun verb pronoun verb adverb adjective infinitive article noun?

proof (1)

cratermoon (765155) | more than 3 years ago | (#35361306)

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 [rollingstone.com] .

Re:proof (1)

Eightbitgnosis (1571875) | more than 3 years ago | (#35361670)

Judging by the number of millionaires who work on Wall Street I'd say their formulas work pretty damn well

Re:proof (1)

cratermoon (765155) | more than 3 years ago | (#35362262)

You make a good point -- perhaps they are Working As Intended, but not economically optimally.

Re:proof (0)

Anonymous Coward | more than 3 years ago | (#35363680)

That's kind of like saying rheumatoid arthritis is proof your immune system is working pretty damn well.

Re:proof (1)

garyebickford (222422) | more than 3 years ago | (#35364136)

I would say that the Quant methods worked very damn well. (The book "Yhe Quants" is fascinating BTW - also "Too Big to Fail" - books on CD = excellent driving amusement). In fact their effect can be seen very well as a classic 'technology bubble'. So also the 'Mortgage Bubble' where a combination of new technology (capitalization of home loans), combined with some regulatory mistakes and a large dose of people-taking-advantage on all sides.

An attempt at an explanation (2)

Luxemburg (890431) | more than 3 years ago | (#35361540)

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/ [intel.com] 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.

Re:An attempt at an explanation (1)

Luxemburg (890431) | more than 3 years ago | (#35361808)

To be more exact, there is no easy formula of the hypergeometric kind, which is a formula "involving binomial coefficients, factorials, rational functions, and power functions" according to http://mathworld.wolfram.com/HypergeometricIdentity.html [wolfram.com] . It would thus theoretically still be possible that an easy formula exists, but it must involve constructions more exotic than that.

Simple (0)

Anonymous Coward | more than 3 years ago | (#35361652)

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."

The Black-Sholes Formula (+1, Helpful ) (0)

Anonymous Coward | more than 3 years ago | (#35361746)

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

Neither does most of physics (1)

jfengel (409917) | more than 3 years ago | (#35361770)

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.

Re:Neither does most of physics (1)

jfengel (409917) | more than 3 years ago | (#35361792)

Not to imply that the work isn't interesting. I'm sure it's got all sorts of implications with respect to the way economists analyze the algorithms. But commenters so far seem to want to jump from "no closed form exists" to "Wall Street is fundamentally unsound", which seems, uh, unsound.

EConned by Yves Smith. (1)

decora (1710862) | more than 3 years ago | (#35362608)

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

Re:EConned by Yves Smith. (1)

jfengel (409917) | more than 3 years ago | (#35362930)

Sure. But the lack of a closed form for this formula doesn't go to demonstrate that.

Re:Neither does most of physics (1)

plopez (54068) | more than 3 years ago | (#35363048)

A good model can take into account corruption.

Re:Neither does most of physics (1)

garyebickford (222422) | more than 3 years ago | (#35364154)

Yes. A better answer would be, "economies are complex adaptive systems" (CAS is a term that essentially means 'living systems') - like neural networks, ecosystems, any biological system, etc.

Classical economics is BS? (0)

Anonymous Coward | more than 3 years ago | (#35361812)

Wow, I am surprised.

An Old and Famous (and not very good method) (1)

ICantFindADecentNick (768907) | more than 3 years ago | (#35362096)

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).

Re:An Old and Famous (and not very good method) (0)

Anonymous Coward | more than 3 years ago | (#35364304)

Yes, applying the binomial model to vanilla European options in practice is pointless; but, it is important to remember that an American option with no dividends is equivalent to a European option with the same parameters. Since the binomial model for said European option admits no closed form in general, we know that the binomial model for American options _in general_ has no closed form.

The actual Deal, If anyone cares (4, Informative)

cb123 (1530513) | more than 3 years ago | (#35362636)

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.

Re:The actual Deal, If anyone cares (0)

Anonymous Coward | more than 3 years ago | (#35362820)

Yes, it cements an old believe with a conclusive proof. And this is significant step.

Unfortunately, now it also diminishes hope of further improvement to that.

Your argument reads like .... (that's an analogy) .... oh ho ... we all new that P!=NP .... but yeah it's good to have a proof, but changes the world not at all .. ;)

Re:The actual Deal, If anyone cares (1)

cb123 (1530513) | more than 3 years ago | (#35362934)

I don't believe you understand the situation or my argument. It's not nearly as strong as P=NP or not. There could be non-hypergeometric family simplifications that do better than the Dai linear sums, and there can be other numerical methods that also do better (and there are for some kinds of options). This new paper just shows that one possible approach to simplify a formula won't work - a formula-to-be-improved already only compelling because Dai et al compare it to naive, strawmen alternatives they found in a textbook, not actual competitive methods available in the options pricing literature. So, it's not a paper to be rejected, but it really doesn't change the world much. It says, "don't look *here* for a way to simplify that other non-optimal approach".

hhgttg (0)

Anonymous Coward | more than 3 years ago | (#35362778)

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.

Load More Comments
Slashdot Login

Need an Account?

Forgot your password?