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As currently written, the second sentence is "From the model, one can deduce the Black–Scholes formula". Hmmm... "deduce"? Really? That phrasing seems muddled, to put it nicely. Quantitative models often *consist of* formulas but rarely "generate" formulas. Isn't it better to say that the B-S model consists of the B-S equation? Hugantik ( talk) 07:30, 9 March 2013 (UTC)
Since the vast majority of options traded today are American-style, why is there no mention of how the BS model needs to be changed to accommodate them? — Preceding unsigned comment added by Hsfrey ( talk • contribs) 04:36, 5 May 2012 (UTC)
The section on Black-Scholes calculators written by User:Novolucidus, which refers to his/her webpage, is based on a misconception. S/he seems unaware that the rate put into Matlab's price function is not the same as the one put into his/her function. Matlab's function requires the rate be continuously compounded while his/her does not. In other words, if Matlab's rate is r, and Novolucidus' rate is R, 1+R = e^r. The use of a continuously compounded interest rate is fairly common in this area, and I expect that's why "the majority of such calculators" do not agree with Novolucidus'. -- C S ( talk) 17:45, 7 August 2012 (UTC)
The material is also a violation of the Wikipedia policy on original research. Since Novolucidus is new to WIkipedia, I doubt s/he is aware of this, which is why I am focusing on showing the flaw in the material. But the policy violation should be pointed out, nonetheless. C S ( talk) 17:55, 7 August 2012 (UTC)
In The Black–Scholes equation, we read
What happened to the term ? If this can be ignored, we should explain why.
S.racaniere ( talk) 14:24, 15 November 2012 (UTC)
For example, we now have some mammoth, garbled explanation in the "interpretation" subsection. It just kept getting longer, and now it is a mash of several different expository threads. The problem with this article is that everyone keeps adding their favorite bit, but nobody wants to clean it up and neatly organize the material.
In the hopes that some of these people read the talk page before adding their material, please STOP. At least give an eye toward cleaning up the article before adding what you'd like. -- C S ( talk) 09:52, 19 January 2013 (UTC)
As the beginnings of an outline, I suggest:
The reason I list the formula first is that i think that's what most layman want to see first. Right now the article starts like a textbook, listing assumptions, then a derivation and so forth. That's not so helpful for most people, and I daresay even those studying the subject for the first time. We should start by showing how the formula makes sense and satisfies consistency checks. I think also emphasizing how the two terms represent a long position in the stock and a short position in the money market is very useful and should help later with the delta-hedging argument. -- C S ( talk) 09:21, 26 February 2013 (UTC)
Here is a proposal for a more concise interpretation section:
The version above connects the first term of the BS formula to the partial expectation of the log-normal distribution, and removes discussion of the numeraire. I think that the concept of numeraire is not particularly intuitive to beginners, while the explanation in terms of the partial expectation of the log-normal does explain the difference between and and allows the reader to easily derive them, provided one accepts that . If we do keep the interpretation in terms of numeraire, we should cite sources that derive it.
References
{{
cite journal}}
: External link in |number=
and |postscript=
(
help)CS1 maint: postscript (
link)
Why isn't C(S, t) = max{S − D K, 0} a solution? u(x, τ) = K [exp(max{x + σ2τ/2, 0}) − 1]. Granted, the first derivatives have a jump at S = D K. Do the sources just assume that the solution has continuous first derivatives or do they require it for some reason?— pivovarov ( talk) 09:07, 12 April 2013 (UTC)
The result of the proposal was moved. -- BDD ( talk) 18:42, 26 November 2013 (UTC)
Black–Scholes →
Black–Scholes model – Per
WP:NOUN: "Nouns and noun phrases are normally preferred over titles using other parts of speech
" and "Adjective and verb forms (e.g. democratic, integrate) should redirect to articles titled with the corresponding noun
". The phrase "Black–Scholes" is an attributive adjective phrase, whereas the article is about the "Black–Scholes model". Since 2009, "
Black–Scholes model" has been a redirect to "
Black–Scholes". (Note that there is a separate article about the
Black–Scholes equation.)
BarrelProof (
talk) 20:20, 17 November 2013 (UTC)
I think the presented price formulas are not correct, the correct ones are available here: http://www.macroption.com/black-scholes-formula/. — Preceding unsigned comment added by 217.173.8.141 ( talk) 22:47, 15 May 2015 (UTC)
Question | Note |
---|---|
There is muddle with terms. | /info/en/?search=Black–Scholes_equation (here we can find C as price and as value) |
Why is known? We don't know the S_T which is geometric Brownian motion, so we cannot calculate (S_T - K).
As I can see, there are 2 options in portfolio: 1st - the short call (sold, written), 2nd -- the long call (bought). So by V(S,T) author means the value of 1st short call. Right? |
/info/en/?search=Black–Scholes_equation
quote: The payoff of an option at maturity is known. |
95.132.143.157 ( talk) 19:13, 22 November 2015 (UTC)
Quote | |
---|---|
Does this help? | Yes. |
The exercise price is the strike price is generally written as but only equals if it is at the money | Suppose someone bought out-of-the-money call option. Price of underlying asset goes up https://img-fotki.yandex.ru/get/3710/240791000.0/0_1a663a_c1a8cc94_orig.gif , but . What should option holder do? He have already paid intrinsic value as part of premium. So he can buy underlying asset at the price less than K. Is it correct? |
the value of the option is equal to its payoff which is known | Option value is the synonym of payoff. This statement can not be the proof. Ok, then why payoff is known? At moment t=0 of option buying only S_0 is known . Or we are reviewing the moment t=TÂ ? |
Let first examine european call option: https://img-fotki.yandex.ru/get/3102/240791000.0/0_1a6662_28c5c637_orig.gif . On this image what is option value, what is payoff, and what is option price? And what actually authors are trying to find by this formula: ( /info/en/?search=Black–Scholes_model) ? And why does not this solution match with solution on this page /info/en/?search=Black–Scholes_equation ? |
92.113.144.245 ( talk) 04:05, 24 November 2015 (UTC)
Can anybody explain me how is next formule obtained  ? First autors use Ito's Lemma and get differential of function which is absolutely unrelated to proving. So differential of any function of 2 variables can be represented as ( http://www.math.tamu.edu/~stecher/425/Sp12/brownianMotion.pdf) . By substituting to and to authors get ( /info/en/?search=Black–Scholes_equation)
But what is next? How do they obtain Black–Scholes equation and  ??? I've heard they use Feynman-Kac formula. But that formula gives expectation value of function, not ready formula. 0.0.0.0 ( talk) 05:49, 26 November 2015 (UTC)
Dr. Wu has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
For the special case of a European call or put option, Black and Scholes showed that "it is possible to create a hedged position, consisting of a long position in the stock and a short position in the option, whose value will not depend on the price of the stock".[5] Their dynamic hedging strategy led to a partial differential equation which governed the price of the option. Its solution is given by the Black–Scholes formula.
Add the following:
The key insight of the model is that one can completely eliminate the risk of the option by dynamically and continuously trading the underlying stock. In practice, one can only trade discretely due to transaction cost. Even so, the risk of an option position can be drastically reduced through hedging with the underlying stock. This insight contributed in a large part to the booming of the derivatives industry.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Wu has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeasBot ( talk) 09:12, 16 June 2016 (UTC)
So everything is for the best in the best of all possible worlds? So folk don't lose their homes, their jobs, their security, and their hope because of abuse of this formula by the banks? So the Nobel Prize was justly awarded? Very reassuring Delahays ( talk) 07:56, 5 November 2017 (UTC)
User: LAA78 SPA is trying to put/market his own software on the Black Scholes Page. He emailed me after revert to say so. An encyclopedia is not a bulletin board. Limit-theorem ( talk) 23:51, 8 January 2018 (UTC)
Good point, C.Fred! Then why do you have a "Computer Implementations" section? Who posted the different links? There are multiple duplicates of the same type of software, which isn't very productive. Lol. Sad. This place is sad. No more Wikipedia donations for me. Can I get my money back? LAA78 —Preceding undated comment added 00:32, 9 January 2018 (UTC)
Please speak English, Limit-theorem. I'm not a millennial. And please address my contention on the implementation issue regarding numerical methods. Do you know anything about numerical methods? LAA78 — Preceding unsigned comment added by 108.48.189.58 ( talk) 02:16, 9 January 2018 (UTC)
I would just like to point out that the model works correctly for time intervals expressed in any unit u as long as interest rates are expressed in 1/u. One needs simply to convert whenever appropriate, just as in any dimensional problem. Specifying that these must be in years is incorrect and confusing. There must be some source which can be cited for this. 50.121.51.32 ( talk) 14:13, 27 February 2019 (UTC)
When the article says (under "Assumptions on the market") "there is no way to make a riskless profit", shouldn't that be "riskless profit greater than the risk-free interest rate"?
Jmichael ll ( talk) 16:33, 10 June 2019 (UTC)
This article has the tone of a math textbook, with instructional language and extensive use of "we". Wikipedia is an encyclopedia, not a textbook. Please see Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_manual,_guidebook,_textbook,_or_scientific_journal.
Ira Ira Leviton ( talk) 14:42, 25 July 2020 (UTC)
The bit with the Black/Scholes formula uses both and as well as and notation interchangeably. Both are possible, but it should be consistent within the article. Smeyen ( talk) 16:59, 31 March 2023 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
As currently written, the second sentence is "From the model, one can deduce the Black–Scholes formula". Hmmm... "deduce"? Really? That phrasing seems muddled, to put it nicely. Quantitative models often *consist of* formulas but rarely "generate" formulas. Isn't it better to say that the B-S model consists of the B-S equation? Hugantik ( talk) 07:30, 9 March 2013 (UTC)
Since the vast majority of options traded today are American-style, why is there no mention of how the BS model needs to be changed to accommodate them? — Preceding unsigned comment added by Hsfrey ( talk • contribs) 04:36, 5 May 2012 (UTC)
The section on Black-Scholes calculators written by User:Novolucidus, which refers to his/her webpage, is based on a misconception. S/he seems unaware that the rate put into Matlab's price function is not the same as the one put into his/her function. Matlab's function requires the rate be continuously compounded while his/her does not. In other words, if Matlab's rate is r, and Novolucidus' rate is R, 1+R = e^r. The use of a continuously compounded interest rate is fairly common in this area, and I expect that's why "the majority of such calculators" do not agree with Novolucidus'. -- C S ( talk) 17:45, 7 August 2012 (UTC)
The material is also a violation of the Wikipedia policy on original research. Since Novolucidus is new to WIkipedia, I doubt s/he is aware of this, which is why I am focusing on showing the flaw in the material. But the policy violation should be pointed out, nonetheless. C S ( talk) 17:55, 7 August 2012 (UTC)
In The Black–Scholes equation, we read
What happened to the term ? If this can be ignored, we should explain why.
S.racaniere ( talk) 14:24, 15 November 2012 (UTC)
For example, we now have some mammoth, garbled explanation in the "interpretation" subsection. It just kept getting longer, and now it is a mash of several different expository threads. The problem with this article is that everyone keeps adding their favorite bit, but nobody wants to clean it up and neatly organize the material.
In the hopes that some of these people read the talk page before adding their material, please STOP. At least give an eye toward cleaning up the article before adding what you'd like. -- C S ( talk) 09:52, 19 January 2013 (UTC)
As the beginnings of an outline, I suggest:
The reason I list the formula first is that i think that's what most layman want to see first. Right now the article starts like a textbook, listing assumptions, then a derivation and so forth. That's not so helpful for most people, and I daresay even those studying the subject for the first time. We should start by showing how the formula makes sense and satisfies consistency checks. I think also emphasizing how the two terms represent a long position in the stock and a short position in the money market is very useful and should help later with the delta-hedging argument. -- C S ( talk) 09:21, 26 February 2013 (UTC)
Here is a proposal for a more concise interpretation section:
The version above connects the first term of the BS formula to the partial expectation of the log-normal distribution, and removes discussion of the numeraire. I think that the concept of numeraire is not particularly intuitive to beginners, while the explanation in terms of the partial expectation of the log-normal does explain the difference between and and allows the reader to easily derive them, provided one accepts that . If we do keep the interpretation in terms of numeraire, we should cite sources that derive it.
References
{{
cite journal}}
: External link in |number=
and |postscript=
(
help)CS1 maint: postscript (
link)
Why isn't C(S, t) = max{S − D K, 0} a solution? u(x, τ) = K [exp(max{x + σ2τ/2, 0}) − 1]. Granted, the first derivatives have a jump at S = D K. Do the sources just assume that the solution has continuous first derivatives or do they require it for some reason?— pivovarov ( talk) 09:07, 12 April 2013 (UTC)
The result of the proposal was moved. -- BDD ( talk) 18:42, 26 November 2013 (UTC)
Black–Scholes →
Black–Scholes model – Per
WP:NOUN: "Nouns and noun phrases are normally preferred over titles using other parts of speech
" and "Adjective and verb forms (e.g. democratic, integrate) should redirect to articles titled with the corresponding noun
". The phrase "Black–Scholes" is an attributive adjective phrase, whereas the article is about the "Black–Scholes model". Since 2009, "
Black–Scholes model" has been a redirect to "
Black–Scholes". (Note that there is a separate article about the
Black–Scholes equation.)
BarrelProof (
talk) 20:20, 17 November 2013 (UTC)
I think the presented price formulas are not correct, the correct ones are available here: http://www.macroption.com/black-scholes-formula/. — Preceding unsigned comment added by 217.173.8.141 ( talk) 22:47, 15 May 2015 (UTC)
Question | Note |
---|---|
There is muddle with terms. | /info/en/?search=Black–Scholes_equation (here we can find C as price and as value) |
Why is known? We don't know the S_T which is geometric Brownian motion, so we cannot calculate (S_T - K).
As I can see, there are 2 options in portfolio: 1st - the short call (sold, written), 2nd -- the long call (bought). So by V(S,T) author means the value of 1st short call. Right? |
/info/en/?search=Black–Scholes_equation
quote: The payoff of an option at maturity is known. |
95.132.143.157 ( talk) 19:13, 22 November 2015 (UTC)
Quote | |
---|---|
Does this help? | Yes. |
The exercise price is the strike price is generally written as but only equals if it is at the money | Suppose someone bought out-of-the-money call option. Price of underlying asset goes up https://img-fotki.yandex.ru/get/3710/240791000.0/0_1a663a_c1a8cc94_orig.gif , but . What should option holder do? He have already paid intrinsic value as part of premium. So he can buy underlying asset at the price less than K. Is it correct? |
the value of the option is equal to its payoff which is known | Option value is the synonym of payoff. This statement can not be the proof. Ok, then why payoff is known? At moment t=0 of option buying only S_0 is known . Or we are reviewing the moment t=TÂ ? |
Let first examine european call option: https://img-fotki.yandex.ru/get/3102/240791000.0/0_1a6662_28c5c637_orig.gif . On this image what is option value, what is payoff, and what is option price? And what actually authors are trying to find by this formula: ( /info/en/?search=Black–Scholes_model) ? And why does not this solution match with solution on this page /info/en/?search=Black–Scholes_equation ? |
92.113.144.245 ( talk) 04:05, 24 November 2015 (UTC)
Can anybody explain me how is next formule obtained  ? First autors use Ito's Lemma and get differential of function which is absolutely unrelated to proving. So differential of any function of 2 variables can be represented as ( http://www.math.tamu.edu/~stecher/425/Sp12/brownianMotion.pdf) . By substituting to and to authors get ( /info/en/?search=Black–Scholes_equation)
But what is next? How do they obtain Black–Scholes equation and  ??? I've heard they use Feynman-Kac formula. But that formula gives expectation value of function, not ready formula. 0.0.0.0 ( talk) 05:49, 26 November 2015 (UTC)
Dr. Wu has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
For the special case of a European call or put option, Black and Scholes showed that "it is possible to create a hedged position, consisting of a long position in the stock and a short position in the option, whose value will not depend on the price of the stock".[5] Their dynamic hedging strategy led to a partial differential equation which governed the price of the option. Its solution is given by the Black–Scholes formula.
Add the following:
The key insight of the model is that one can completely eliminate the risk of the option by dynamically and continuously trading the underlying stock. In practice, one can only trade discretely due to transaction cost. Even so, the risk of an option position can be drastically reduced through hedging with the underlying stock. This insight contributed in a large part to the booming of the derivatives industry.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Wu has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeasBot ( talk) 09:12, 16 June 2016 (UTC)
So everything is for the best in the best of all possible worlds? So folk don't lose their homes, their jobs, their security, and their hope because of abuse of this formula by the banks? So the Nobel Prize was justly awarded? Very reassuring Delahays ( talk) 07:56, 5 November 2017 (UTC)
User: LAA78 SPA is trying to put/market his own software on the Black Scholes Page. He emailed me after revert to say so. An encyclopedia is not a bulletin board. Limit-theorem ( talk) 23:51, 8 January 2018 (UTC)
Good point, C.Fred! Then why do you have a "Computer Implementations" section? Who posted the different links? There are multiple duplicates of the same type of software, which isn't very productive. Lol. Sad. This place is sad. No more Wikipedia donations for me. Can I get my money back? LAA78 —Preceding undated comment added 00:32, 9 January 2018 (UTC)
Please speak English, Limit-theorem. I'm not a millennial. And please address my contention on the implementation issue regarding numerical methods. Do you know anything about numerical methods? LAA78 — Preceding unsigned comment added by 108.48.189.58 ( talk) 02:16, 9 January 2018 (UTC)
I would just like to point out that the model works correctly for time intervals expressed in any unit u as long as interest rates are expressed in 1/u. One needs simply to convert whenever appropriate, just as in any dimensional problem. Specifying that these must be in years is incorrect and confusing. There must be some source which can be cited for this. 50.121.51.32 ( talk) 14:13, 27 February 2019 (UTC)
When the article says (under "Assumptions on the market") "there is no way to make a riskless profit", shouldn't that be "riskless profit greater than the risk-free interest rate"?
Jmichael ll ( talk) 16:33, 10 June 2019 (UTC)
This article has the tone of a math textbook, with instructional language and extensive use of "we". Wikipedia is an encyclopedia, not a textbook. Please see Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_manual,_guidebook,_textbook,_or_scientific_journal.
Ira Ira Leviton ( talk) 14:42, 25 July 2020 (UTC)
The bit with the Black/Scholes formula uses both and as well as and notation interchangeably. Both are possible, but it should be consistent within the article. Smeyen ( talk) 16:59, 31 March 2023 (UTC)