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It is possible to use various finite difference methods for both American and Bermudan options (It's an assignment to write such a program in my numerical methods class.). While it is also true that the binomial tree model can accommodate discrete dividends, so can these finite difference methods. Why do you think that binary trees are "more accuratte"? Eweinber ( talk) 14:53, 27 October 2010 (UTC)
I reverted a change by 59.162.216.53 that claimed the binomial model is impractical. This is not true. By in large, the binomial model is used by practioners for a variety of reasons, mostly having to do with accuracy. As a developer of quantitative option pricing models, I have a fairly broad exposure to this issue and have yet to come across a serious option trader relying on the Black-Scholes model for actual trading. Ronnotel 13:25, 27 September 2006 (UTC)
I believe most practical binomial models use discrete dividends rather than a continuous dividend yield. Using a continuous dividend yield can result in significant mis-pricing at or near dividend dates. Any objections to changing the formula to reflect this? Ronnotel 16:55, 28 November 2006 (UTC)
I was using this article as a guideline for constructing a simple binomial model for valuing a stock option and came across an interesting problem/issue/quirkiness/something. I would get all my values do up the formula and I realized that when I changed the value for the volatility of the stock the end result did not change at all. Not even by the lowliest of decimal points. After reducing the formulae for the binomial value and the probability, p, I found out why.
The formula for the binomial value given in the ariticle is equivalent to
where:
S is the current price of the underlying
q is the dividend yield
t is the time step
(I hope I've given the correct key, all the variables above correspond to those in the article).
Why then, would the formula and the model require so much information if you only really need these three things? Is there a mistake somewhere in there maybe?
Or am I just making things up?
Douglas Robinson 18:28, 29 November 2006 (UTC)
Binomial Formula
=pSu+(1-p)Sd)/(e^{rt})
=S(p({u-d}/{e^{rt}})+d/e^{rt})
=S({e^{(r-q)t+sigma*sqrt(t)}-1}/{e^{2sigma*sqrt(t)}-1}(e^{sigma*sqrt(t)-rt}-e^{-sigma*sqrt(t) -rt})=d/{e^{rt}})
=S({e^{-qt+2*sigma*sqrt(t)}-e^{-qt}}/{e^{2*sigma*sqrt(t)}-1}
=Se^{-qt}({e^{2*sigma*sqrt{t}}-1}/{e^{2*sigma*sqrt{t}}-1})
=Se^{-qt}
(Sorry for the confusing look of it, but I couldn't quite get the syntax of the math parser)
Douglas Robinson 21:43, 29 November 2006 (UTC)
I think your approach is a little off - you are using stock price (S) where you should be using option prices (C). Start with two trees, one filled with stock prices (S), the other with option prices (C). The stock prices are easy, base node is just S(0). Next step has Su and Sd. Third step has Suu, S(0) and Sdd, etc. Now, start filling in the option tree from back to front. The last step is also easy, just calculate expiration value of the option for each stock price from the stock tree. Next, go back one time step in the option tree using the binomial formula. However, use the values from the option tree, i.e.
Ronnotel 21:53, 29 November 2006 (UTC)
Okay,
I definitely have been approaching the model in the wrong way. Thanks for clearing that up for me. But the formula still has that weirdness to it.
If you start with
You can continue with:
(going to try out this math parser again... had a nice image of the equation and working out but I don't see how to upload it)
Douglas Robinson 15:09, 30 November 2006 (UTC)
I think I see a problem, please note that is not the same as . can only be calculated through the backward induction step described above. Again, I would strongly encourage you to get ahold of either of the references I mentioned - going off this article alone is going to be a tough journey. Ronnotel 15:16, 30 November 2006 (UTC)
User:Jesse 20/09/2013 Hey, I've just implemented this algorithm in Matlab, and it's apparent that the exercise price at time t is NEVER more than the expected price from the two possible branches at time t+dt, which means the time zero American call is always valued identically to the European call. — Preceding unsigned comment added by 130.130.37.85 ( talk) 05:15, 20 September 2013 (UTC)
User:Jesse 21/09/2013
I've since learned that without any dividends, the above mentioned call values are in fact the same. — Preceding unsigned comment added by 101.161.174.12 ( talk) 01:18, 21 September 2013 (UTC)
In section Computer Implementations of this article there is a list of spreadsheets:
1st: page doesn't work (some PHP Zend Optimizer problem).
2nd and 3rd: xls files don't work in MS Office 2007, because macros need that the cells are unlocked to work, but IDK the password to unlock them. Perhaps it works in older Excel versions - IDK this and i can't check.
Maybe this section should be revised?
--
Loonatic (
talk)
21:48, 18 December 2010 (UTC)
I have no particular issue with discussing the recent paper proving no closed-form solution (CFS) in the article. However, in order to feature this result (should it hold up to scrutiny, no particular doubt that it won't) in very first paragraph would require some evidence that the world of quantitative finance has been searching for a closed-form solution to BOPM. I'm a practitioner in this exact field with too many years of experience to mention and I can't recall reading about anyone ever searching for such a thing. In my experience, it's always been assumed that one didn't exist although I suppose it's nice to know that no-one has wasted their time looking, I guess. Is there reliably sourced evidence of a search for a CFS to BOPM? Ronnotel ( talk) 17:00, 2 March 2011 (UTC)
However, in order to feature this result (should it hold up to scrutiny, no particular doubt that it won't) in very first paragraph would require some evidence that the world of quantitative finance has been searching for a closed-form solution to BOPM.
Aha! I agree but such evidence will almost surely have failed to surface given failed attempts of obtaining a closed form solution unless they would come in form of a conclusive proof; such is the result of this paper. (Conceivably, failed attempts would have not been worthy of publications). Additionally, this result cements in an elegant manner your belief that none exists. It should be worthy to be mentioned in the very first paragraph as it highlights BOPMs limitations. — Preceding unsigned comment added by Algotheorist ( talk • contribs) 18:27, 2 March 2011 (UTC)
Almost there! just as we enlist the authors of BOPM by name, it would be only be honorable to give the author what he deserves in that context. In general, Georgiadis in xxrefxx proves that binomial options pricing models do not have closed-form solutions. — Preceding unsigned comment added by Algotheorist ( talk • contribs) 19:43, 2 March 2011 (UTC)
{{edit semi-protected}}
Please remove the vanity reference to Georgiadis's paper in note 1. It is an uninteresting result that has no significance, since the limit of the binomial model is the Black-Scholes formula and there are no computational complexity problems at all. This reference to Georgiadis does not deserve to be there and will distract readers trying to learn something about the binomial model.
207.237.215.140 ( talk) 13:31, 7 March 2011 (UTC) 13:31, 7 March 2011 (UTC) 207.237.215.140 ( talk)
Interesting. I have been a quant /trader and have been in this industry for a decade. The result seems worth keeping because it is significant enough. 207.237.215.140 I think your point gets addressed in the article if you cared reading it, I think.This comment is from a new account that has been indefinitely blocked as a suspected sock puppet of another user. Ronnotel ( talk) 14:41, 8 March 2011 (UTC)
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Hopefully, someone will update this entry to illustrate practical examples of how to use the Binomial model.
For example, I want to price an equity option (American style) where the underlying pays a dividend. How do I use this model? Say the options expires in 9 months, and 2 dividends are due between today and expiration. Also, how does one determine how many steps to use? The more the better? The difference in a call's price between say using 10 steps and 100 steps is significant.
Basically, in other words, how does a speculator use this model? — Preceding unsigned comment added by Floyd2012 ( talk • contribs) 23:02, 29 November 2020 (UTC)
What does the term sigma do in the algorithm?
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
It is possible to use various finite difference methods for both American and Bermudan options (It's an assignment to write such a program in my numerical methods class.). While it is also true that the binomial tree model can accommodate discrete dividends, so can these finite difference methods. Why do you think that binary trees are "more accuratte"? Eweinber ( talk) 14:53, 27 October 2010 (UTC)
I reverted a change by 59.162.216.53 that claimed the binomial model is impractical. This is not true. By in large, the binomial model is used by practioners for a variety of reasons, mostly having to do with accuracy. As a developer of quantitative option pricing models, I have a fairly broad exposure to this issue and have yet to come across a serious option trader relying on the Black-Scholes model for actual trading. Ronnotel 13:25, 27 September 2006 (UTC)
I believe most practical binomial models use discrete dividends rather than a continuous dividend yield. Using a continuous dividend yield can result in significant mis-pricing at or near dividend dates. Any objections to changing the formula to reflect this? Ronnotel 16:55, 28 November 2006 (UTC)
I was using this article as a guideline for constructing a simple binomial model for valuing a stock option and came across an interesting problem/issue/quirkiness/something. I would get all my values do up the formula and I realized that when I changed the value for the volatility of the stock the end result did not change at all. Not even by the lowliest of decimal points. After reducing the formulae for the binomial value and the probability, p, I found out why.
The formula for the binomial value given in the ariticle is equivalent to
where:
S is the current price of the underlying
q is the dividend yield
t is the time step
(I hope I've given the correct key, all the variables above correspond to those in the article).
Why then, would the formula and the model require so much information if you only really need these three things? Is there a mistake somewhere in there maybe?
Or am I just making things up?
Douglas Robinson 18:28, 29 November 2006 (UTC)
Binomial Formula
=pSu+(1-p)Sd)/(e^{rt})
=S(p({u-d}/{e^{rt}})+d/e^{rt})
=S({e^{(r-q)t+sigma*sqrt(t)}-1}/{e^{2sigma*sqrt(t)}-1}(e^{sigma*sqrt(t)-rt}-e^{-sigma*sqrt(t) -rt})=d/{e^{rt}})
=S({e^{-qt+2*sigma*sqrt(t)}-e^{-qt}}/{e^{2*sigma*sqrt(t)}-1}
=Se^{-qt}({e^{2*sigma*sqrt{t}}-1}/{e^{2*sigma*sqrt{t}}-1})
=Se^{-qt}
(Sorry for the confusing look of it, but I couldn't quite get the syntax of the math parser)
Douglas Robinson 21:43, 29 November 2006 (UTC)
I think your approach is a little off - you are using stock price (S) where you should be using option prices (C). Start with two trees, one filled with stock prices (S), the other with option prices (C). The stock prices are easy, base node is just S(0). Next step has Su and Sd. Third step has Suu, S(0) and Sdd, etc. Now, start filling in the option tree from back to front. The last step is also easy, just calculate expiration value of the option for each stock price from the stock tree. Next, go back one time step in the option tree using the binomial formula. However, use the values from the option tree, i.e.
Ronnotel 21:53, 29 November 2006 (UTC)
Okay,
I definitely have been approaching the model in the wrong way. Thanks for clearing that up for me. But the formula still has that weirdness to it.
If you start with
You can continue with:
(going to try out this math parser again... had a nice image of the equation and working out but I don't see how to upload it)
Douglas Robinson 15:09, 30 November 2006 (UTC)
I think I see a problem, please note that is not the same as . can only be calculated through the backward induction step described above. Again, I would strongly encourage you to get ahold of either of the references I mentioned - going off this article alone is going to be a tough journey. Ronnotel 15:16, 30 November 2006 (UTC)
User:Jesse 20/09/2013 Hey, I've just implemented this algorithm in Matlab, and it's apparent that the exercise price at time t is NEVER more than the expected price from the two possible branches at time t+dt, which means the time zero American call is always valued identically to the European call. — Preceding unsigned comment added by 130.130.37.85 ( talk) 05:15, 20 September 2013 (UTC)
User:Jesse 21/09/2013
I've since learned that without any dividends, the above mentioned call values are in fact the same. — Preceding unsigned comment added by 101.161.174.12 ( talk) 01:18, 21 September 2013 (UTC)
In section Computer Implementations of this article there is a list of spreadsheets:
1st: page doesn't work (some PHP Zend Optimizer problem).
2nd and 3rd: xls files don't work in MS Office 2007, because macros need that the cells are unlocked to work, but IDK the password to unlock them. Perhaps it works in older Excel versions - IDK this and i can't check.
Maybe this section should be revised?
--
Loonatic (
talk)
21:48, 18 December 2010 (UTC)
I have no particular issue with discussing the recent paper proving no closed-form solution (CFS) in the article. However, in order to feature this result (should it hold up to scrutiny, no particular doubt that it won't) in very first paragraph would require some evidence that the world of quantitative finance has been searching for a closed-form solution to BOPM. I'm a practitioner in this exact field with too many years of experience to mention and I can't recall reading about anyone ever searching for such a thing. In my experience, it's always been assumed that one didn't exist although I suppose it's nice to know that no-one has wasted their time looking, I guess. Is there reliably sourced evidence of a search for a CFS to BOPM? Ronnotel ( talk) 17:00, 2 March 2011 (UTC)
However, in order to feature this result (should it hold up to scrutiny, no particular doubt that it won't) in very first paragraph would require some evidence that the world of quantitative finance has been searching for a closed-form solution to BOPM.
Aha! I agree but such evidence will almost surely have failed to surface given failed attempts of obtaining a closed form solution unless they would come in form of a conclusive proof; such is the result of this paper. (Conceivably, failed attempts would have not been worthy of publications). Additionally, this result cements in an elegant manner your belief that none exists. It should be worthy to be mentioned in the very first paragraph as it highlights BOPMs limitations. — Preceding unsigned comment added by Algotheorist ( talk • contribs) 18:27, 2 March 2011 (UTC)
Almost there! just as we enlist the authors of BOPM by name, it would be only be honorable to give the author what he deserves in that context. In general, Georgiadis in xxrefxx proves that binomial options pricing models do not have closed-form solutions. — Preceding unsigned comment added by Algotheorist ( talk • contribs) 19:43, 2 March 2011 (UTC)
{{edit semi-protected}}
Please remove the vanity reference to Georgiadis's paper in note 1. It is an uninteresting result that has no significance, since the limit of the binomial model is the Black-Scholes formula and there are no computational complexity problems at all. This reference to Georgiadis does not deserve to be there and will distract readers trying to learn something about the binomial model.
207.237.215.140 ( talk) 13:31, 7 March 2011 (UTC) 13:31, 7 March 2011 (UTC) 207.237.215.140 ( talk)
Interesting. I have been a quant /trader and have been in this industry for a decade. The result seems worth keeping because it is significant enough. 207.237.215.140 I think your point gets addressed in the article if you cared reading it, I think.This comment is from a new account that has been indefinitely blocked as a suspected sock puppet of another user. Ronnotel ( talk) 14:41, 8 March 2011 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Binomial options pricing model. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
{{
dead link}}
tag to
http://www.bus.lsu.edu/academics/finance/faculty/dchance/Research/ASynthesisofBinomialOptionPricingModels.pdfWhen you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 21:04, 2 November 2016 (UTC)
Hopefully, someone will update this entry to illustrate practical examples of how to use the Binomial model.
For example, I want to price an equity option (American style) where the underlying pays a dividend. How do I use this model? Say the options expires in 9 months, and 2 dividends are due between today and expiration. Also, how does one determine how many steps to use? The more the better? The difference in a call's price between say using 10 steps and 100 steps is significant.
Basically, in other words, how does a speculator use this model? — Preceding unsigned comment added by Floyd2012 ( talk • contribs) 23:02, 29 November 2020 (UTC)
What does the term sigma do in the algorithm?