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Topic Title: American Option Approximation: Which one is better?
Created On Thu Nov 13, 08 02:04 PM
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nuclph
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Thu Nov 13, 08 02:04 PM
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Dear all,

I have several ways in my disposal to get approximated price for American call/put options:

1. Barone-Adesi, G. & Whaley, R (1987)
2. Bjerksund, P. & Stensland, G. (1993)
3. Bjerksund, P. & Stensland, G.(2002)

Questions:

1. Which one is better to use?
2. To get Greeks, I assume I need to use just simple finite difference ?

For example,

Asset price ( S ) 3.50
Strike price ( X ) 3.00
Time to maturity ( T ) 1.5000
Risk-free rate ( r ) 2.50%
Cost of carry ( b ) 0.00%
Volatility ( s ) 55.00%

Price: (Barone-Adesi, G. & Whaley 1987) 1.0996
Price: (Bjerksund, P. & Stensland, G. (1993)) 1.0913
Price: (Bjerksund, P. & Stensland, G. (2002)) 1.0909




 
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spursfan
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Thu Nov 13, 08 03:56 PM
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So you plan to value American calls with 55% volatility and you propose to use one of 3 not very accurate methods

The best instant algorithm is Ju and Zhong (improved version of MBAW) 1.0964
A decent LR binomial tree with extrapolation 1.0976
 
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nuclph
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Thu Nov 13, 08 11:20 PM
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Thank you for suggestions, I did not know about Ju & Zhong work.
My binomial tree also gives 1.0976.
 
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acastaldo
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Sat Nov 15, 08 10:04 PM
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Quote

The best instant algorithm is Ju and Zhong (improved version of MBAW)


Thank you Spursfan for suggesting this on Wilmott some time ago. It has been working well for me and, best of all, it required very little work to implement by modification of my previous MBAW code.

[Added 2008/11/15 9:53pm]:

The Ju Zhong paper can be found on Prof. Ju's website. A quick summary can also be found on Global Derivatives.

Edited: Sun Nov 16, 08 at 02:55 AM by acastaldo
 
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mj
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Tue Nov 18, 08 03:47 AM
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The Tian 3rd moment matching tree with smoothing and extrapolation and truncation is the best method i've found.


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