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JoyPathak
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Joined: September 30th, 2010, 5:55 pm

American Option Approximation

December 7th, 2010, 11:04 pm

http://www.rhsmith.umd.edu/faculty/nju/JZ99JD.pdfIf you goto page 3 it says that the Barone-Adesi/Whaley approximation is good for short maturities since 1-h is close to zero and for long maturities since g/h is close to zero. Maybe I missed something but I do not understand why they would be zero? Can anyone help me out?Thanks in advance!
 
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Hansi
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Joined: January 25th, 2010, 11:47 am

American Option Approximation

December 7th, 2010, 11:35 pm

I'm a bit tired but with tau = T-t and h(tau) = 1-exp(-r*tau), dh(tau) = r*exp(-r*tau)I'd assume that lim[tau -> 0] (1-h(tau)) = 0 and lim[tau -> inf] (dg/dh(tau)) = 0 be the case for r>0.Haven't read the paper but I'm assuming they ignore r<0 and possibly supply a specific case for r=0?
 
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JoyPathak
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American Option Approximation

December 8th, 2010, 2:46 am

QuoteOriginally posted by: HansiI'm a bit tired but with tau = T-t and h(tau) = 1-exp(-r*tau), dh(tau) = r*exp(-r*tau)I'd assume that lim[tau -> 0] (1-h(tau)) = 0 and lim[tau -> inf] (dg/dh(tau)) = 0 be the case for r>0.Haven't read the paper but I'm assuming they ignore r<0 and possibly supply a specific case for r=0?lim[tau -> 0] (1-h(tau)) = 1 because exp goes to 1.. so it's basicaly 1- (1 - 1). Atleast I think. I don't see how it goes to 0? Am I missing something?
 
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Hansi
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Joined: January 25th, 2010, 11:47 am

American Option Approximation

December 8th, 2010, 3:16 am

Nope, you are right. As I mentioned I was tired.
 
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JoyPathak
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American Option Approximation

December 8th, 2010, 3:37 am

QuoteOriginally posted by: HansiNope, you are right. As I mentioned I was tired.Not a problem. Thank you anyways.
 
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tags
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Joined: February 21st, 2010, 12:58 pm

American Option Approximation

December 9th, 2010, 11:19 pm

i must miss something, too ... getting 1- (1-1) = 1 but not 0 just as the text implies
 
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paaatrik
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American Option Approximation

December 21st, 2010, 3:28 pm

In the original paper, http://reference.kfupm.edu.sa/content/e ... 34.pdf"For commodity options with very short (long) times to expiration, this assumption is reasonable since, as T approaches 0 (infinity), fk approaches 0 (K approaches 1) and the term disappears"
 
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quantifyMe
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American Option Approximation

June 1st, 2011, 9:25 pm

reviving an old thread... [Barone-Adesi Whaley model]Can someone please explain why as T -> 0, fk (in Barone-Adesi,Whaley; or gh in Ju,Zhong) -> 0 ?
 
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kanjuo
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American Option Approximation

June 7th, 2011, 7:59 pm

Could someone help me choose an initial guess for an PSOR algorithm for american options, wilmott and Denwyne choose x(0) = max(h(m+1,n);theta(m,n)) in their paper:asian options as linear complementarity problems: analysis and finite diffrence solutions, on page 168. My problem is that both h(m+1,n) and theta(m,n) dont seem to be known a priori...