Ayache and Forsyth - Convertible Bond models

[Joseph Wang]

I downloaded the papers that Ayache and Forsyth wrote on their PDE
convertible, and it looks pretty straight forward to implement once we
have the convertible bond instrument done.  The nice thing about A and F
is that it has some default models that let you get away with doing the
calculation with only one PDE rather than two.  Their full default model
requires two PDE's, but I can implement the simpler one equation default
model as a half step.

That still doesn't solve the problem of the boundary condition that
requires the stock price be less or more than some amount for a given
number of days, but I suspect that this could be put in as an odd
boundary condition.  I was wondering if anyone knows if this problem has
been worked out, or have I found myself at a cutting edge.

[Xavier.Abulker]

Joseph,
There is a reference for that in Risk magazine "the chalenge of equity derivatives, RISK, technology supplement, pages, S29-31 August 1999"
I found that in http://www.defaultrisk.com/pdf__files/Convertivle%20Bonds%20w%20Mkt%20Rsk%20&%20Cr%20Rsk.pdf
"The path dependency of Japanese resettable convertible bonds is handled by Monte-Carlo but since convertible are American style instruments modelling on a tree seems appropriate"
Xavier

Joseph Wang <[hidden email]> Sent by: [hidden email] 28/03/2005 02:47

To:        [hidden email]         cc:                 Subject:        [Quantlib-users] Ayache and Forsyth - Convertible Bond models

I downloaded the papers that Ayache and Forsyth wrote on their PDE
convertible, and it looks pretty straight forward to implement once we
have the convertible bond instrument done.  The nice thing about A and F
is that it has some default models that let you get away with doing the
calculation with only one PDE rather than two.  Their full default model
requires two PDE's, but I can implement the simpler one equation default
model as a half step.

That still doesn't solve the problem of the boundary condition that
requires the stock price be less or more than some amount for a given
number of days, but I suspect that this could be put in as an odd
boundary condition.  I was wondering if anyone knows if this problem has
been worked out, or have I found myself at a cutting edge.




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