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AbhinavBajpai
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Recombining Trinomial Tree

June 13th, 2017, 11:17 am

Please suggest a book/paper which discusses recombining Trinomial tree approach for pricing American options in detail. 
 
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DavidJN
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Re: Recombining Trinomial Tree

June 13th, 2017, 3:33 pm

Tian “A Modified Lattice Approach to Option Pricing”, Journal of Futures Markets, Vol. 13, 1993.
 
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outrun
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Re: Recombining Trinomial Tree

June 13th, 2017, 6:59 pm

"Truncation And Acceleration Of The Tian Tree For The Pricing Of American Put Options"

Ting Chen, Mark Joshi

https://papers.ssrn.com/sol3/papers.cfm ... id=1567218
 
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Cuchulainn
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Re: Recombining Trinomial Tree

June 14th, 2017, 11:33 am

Is there a compelling reason (supervisor demands it, legacy code) to use trinomial? (it is only a simple explicit FDM,  1st order accurate and conditionally stable).

Why not go the whole way and use Crank Nicolson. And it allows you to calculate the greeks in one sweep.

 https://mhittesdorf.wordpress.com/2013/ ... dividends/

I don't see any (e.g. mathematical) reason to use trinomial against a decent FD scheme.

//
One issue I've noticed: I coded Richardson extrapolation for binomial method but I did not get what I expected. I am rather sceptical of the mathematical applicability of RE for lattice models. You just cannot ignore discontinuous payoffs...
See

https://kluedo.ub.uni-kl.de/frontdoor/i ... docId/2166
http://www.datasimfinancial.com
http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
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mj
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Re: Recombining Trinomial Tree

June 28th, 2017, 1:17 am

See also 

Chan, Jiun Hong and Joshi, Mark S. and Tang, Robert and Yang, Chao, Trinomial or Binomial: Accelerating American Put Option Price on Trees (September 1, 2008). Available at SSRN: https://ssrn.com/abstract=1261745 or http://dx.doi.org/10.2139/ssrn.1261745

RE works if the pay-off is smoothed or the tree is adapted to the strike.
 
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Cuchulainn
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Re: Recombining Trinomial Tree

June 28th, 2017, 9:16 am

Indeed. But is a bit of extra preprocessing. 
From a FDM point of view, it probably means trinomial is just A-stable (like Crank Nicolson) I suspect and spurious eigenvalues decay slowly unless some kind of smoothing is performed.
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
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Collector
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Joined: August 21st, 2001, 12:37 pm

Re: Recombining Trinomial Tree

August 6th, 2017, 8:20 pm

Is there a compelling reason (supervisor demands it, legacy code) to use trinomial? (it is only a simple explicit FDM,  1st order accurate and conditionally stable).

Why not go the whole way and use Crank Nicolson. And it allows you to calculate the greeks in one sweep.

 https://mhittesdorf.wordpress.com/2013/ ... dividends/

I don't see any (e.g. mathematical) reason to use trinomial against a decent FD scheme.
Trees: More beautiful Geometry! 
Trees More Interesting History, read the rings!
Tree models more intuitive?

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