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Koala
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Bermudan Options

May 25th, 2003, 8:11 am

Anyone could suggest some readings (books or articles) regarding the hedging and pricing of Bermudan Options???Thx!!!
 
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Stefanone
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Bermudan Options

May 25th, 2003, 10:51 am

On Interest Rate Bermudan Swaptions, have a look at the following, which represents kind of "most popular" approcah to price bermudan:1) Andersen, L. (1998), “A Simple Approach to Pricing of Bermudan Swaptions in the Multi-Factor Libor Market Model,” Working Paper, General Re Financial Products.2) Pedersen, M. (1999), “Bermudan Swaptions in the Libor Market Model,”Working Paper, SimCorp A/S.3) Longstaff, F., and E. Schwartz,"Valuing American Options By Simulation: A Simple Least-Squares Approach,"On textbooks, u can have a look at Brigo-Mercurio, which gives you hints on the implementation of 1) and 3) and presents the bermudan swaption pricing technique within short rate models...Hope it helps,S.
 
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mrbadguy
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Bermudan Options

May 26th, 2003, 12:19 pm

In addition to very appreciated papers indicated by Stefanone, try this paper about pricing of Bermudan Swaptions, try a search on rebonato.com and other LMM (libor market model) sites like Mercurio and Brigo
 
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Balmung
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Bermudan Options

May 27th, 2003, 6:42 am

For more interesting references have a look athttp://www.cmap.polytechnique.fr/~gobet/americaine.htmlRegards
 
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ppauper
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Bermudan Options

April 8th, 2013, 5:39 pm

the delta of a bermudan (equity call under Black-Scholes) option is what, between 0 and 1.Is anyone here smart enough to give a very brief argument in words as to exactly why that is so ?
 
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Alan
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Bermudan Options

April 8th, 2013, 6:00 pm

I think the argument would go something like this.First, for a vanilla call with payoff g(S) there are some standard results that you would have to gothrough that show that the delta must lie in between the minimum slope of g(S) and the maximumslope of g(S). This proves it for the last expiration period of the Bermudan. But then forany earlier expiration period, it proves it also because now the g(S) in question is thevalue of an option which has already been shown to have delta in [0,1]. So the slope ofthat g(S) is the delta of the already-determined solution.
 
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ppauper
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Bermudan Options

April 8th, 2013, 7:37 pm

thanks, that's a start.This is for a paper on a numerical method, and I've been asked by a referee to explain why the price of the option on an exercise date only cuts the payoff line max(S-X,0) once (or twice if you count S=0), and my answer is because the delta is between 0 and 1 so it can't cross more than once, which requires me to explain in turn why the delta....
 
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Alan
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Bermudan Options

April 8th, 2013, 8:09 pm

You're welcome. You can cite Theorem 1 here for the first part of my argument.
 
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ppauper
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Bermudan Options

April 8th, 2013, 9:34 pm

thanks again
 
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mj
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Bermudan Options

April 10th, 2013, 9:47 am

an alternate approach might be that the value is convex and so the second derivative is positive.
 
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deimanteR
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Bermudan Options

April 10th, 2013, 3:00 pm

I think it also follows straightforwardly from the Bermudan option representation via stopping times.
 
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ppauper
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Bermudan Options

April 10th, 2013, 3:05 pm

mj and deimanteR: thanks
 
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Alan
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Bermudan Options

April 10th, 2013, 4:05 pm

QuoteOriginally posted by: mjan alternate approach might be that the value is convex and so the second derivative is positive.Yeah, but that would still admit Delta > 1, which ppauper needs to rule out if I am mentally picturing the issue correctly.
Last edited by Alan on April 9th, 2013, 10:00 pm, edited 1 time in total.
 
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ppauper
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Bermudan Options

April 10th, 2013, 5:11 pm

thanks, Delta>1 would be bad as it would lead to multiple crossings of the pay-off curve
 
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mj
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Bermudan Options

April 11th, 2013, 12:51 am

deeply in the money, the value would be like S_T - K so delta would one and deeply out it would be zero, so it would have to be in between everywhere.