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londoner
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Best Numerical Method for American Put

March 28th, 2008, 10:24 pm

Anyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.
 
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Cuchulainn
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Best Numerical Method for American Put

March 29th, 2008, 10:06 am

QuoteOriginally posted by: londonerAnyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.Define best
 
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umvue
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Best Numerical Method for American Put

March 29th, 2008, 11:48 am

If the best means the simplest, then Binomial Tree.
 
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TraderJoe
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Best Numerical Method for American Put

March 29th, 2008, 1:31 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: londonerAnyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.Define bestConvergence, speed and accuracy - the usual suspects.
 
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Cuchulainn
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Best Numerical Method for American Put

March 29th, 2008, 2:35 pm

QuoteOriginally posted by: TraderJoeQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: londonerAnyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.Define bestConvergence, speed and accuracy - the usual suspects.Bingo!And when all these quality characteristics are realised, software maintainability becomes paramount, at least in complex applications.But many applications don't start life with maintenance in mindISO9126 QuoteConvergence, speed and accuracyOk, what are the best methods for American options?
Last edited by Cuchulainn on March 28th, 2008, 11:00 pm, edited 1 time in total.
 
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TraderJoe
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Best Numerical Method for American Put

March 29th, 2008, 4:22 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: TraderJoeQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: londonerAnyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.Define bestConvergence, speed and accuracy - the usual suspects.Bingo!And when all these quality characteristics are realised, software maintainability becomes paramount, at least in complex applications.But many applications don't start life with maintenance in mindISO9126 QuoteConvergence, speed and accuracyOk, what are the best methods for American options?Monte Carlo. Followed by trees, followed by FDM (Crank-Nicolson).Cheers.
 
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Cuchulainn
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Best Numerical Method for American Put

March 29th, 2008, 6:30 pm

QuoteOriginally posted by: TraderJoeQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: TraderJoeQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: londonerAnyone can suggest which numerical method works best for computing the value of an american put option? e.g. least-square, duality, etc.Define bestConvergence, speed and accuracy - the usual suspects.Bingo!And when all these quality characteristics are realised, software maintainability becomes paramount, at least in complex applications.But many applications don't start life with maintenance in mindISO9126 QuoteConvergence, speed and accuracyOk, what are the best methods for American options?Monte Carlo. Followed by trees, followed by FDM (Crank-Nicolson).Cheers.Also sprach Trader Joe Who agrees? disagrees?
Last edited by Cuchulainn on March 28th, 2008, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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Best Numerical Method for American Put

March 29th, 2008, 6:39 pm

So, we have schemesMCTreesFDM(Quasi) exactThe question to be posed is:How much effort is needed to realise a given accuracy, let's say 10^-3Is this a good, objective test?
Last edited by Cuchulainn on March 28th, 2008, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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Best Numerical Method for American Put

March 30th, 2008, 10:45 am

QuoteOriginally posted by: outrunQuoteOriginally posted by: CuchulainnSo, we have schemesMCTreesFDM(Quasi) exactThe question to be posed is:How much effort is needed to realise a given accuracy, let's say 10^-3Is this a good, objective test?Yes, in which case the list is upside down.I would say that Quasi exact -a FDM + analytical control variate- would be best for the Am put. next FDM above a tree, because a tree is a specific FDM (eurler, forward), and finally MC. MC does not compete very well at low dimensions like, nor at problems where the derivative value depends on the future value of the derivative.This has some results http://www.wilmott.com/messageview.cfm? ... BLE=">here
 
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TraderJoe
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Best Numerical Method for American Put

March 30th, 2008, 2:45 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: outrunQuoteOriginally posted by: CuchulainnSo, we have schemesMCTreesFDM(Quasi) exactThe question to be posed is:How much effort is needed to realise a given accuracy, let's say 10^-3Is this a good, objective test?Yes, in which case the list is upside down.I would say that Quasi exact -a FDM + analytical control variate- would be best for the Am put. next FDM above a tree, because a tree is a specific FDM (eurler, forward), and finally MC. MC does not compete very well at low dimensions like, nor at problems where the derivative value depends on the future value of the derivative.This has some results http://www.wilmott.com/messageview.cfm? ... ">hereSome nice results and discussion. However your link has an error. It should point to here..
 
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Cuchulainn
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Best Numerical Method for American Put

March 30th, 2008, 4:24 pm

 
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TraderJoe
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Best Numerical Method for American Put

March 30th, 2008, 9:55 pm

And his trusty sidekick (yet another physicist) Phyliss.
 
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mj
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Best Numerical Method for American Put

March 31st, 2008, 5:12 am

you can find my detailed analysis of 220 different tree methods for pricing american puts on www.markjoshi.com