Hi
I'm a little disconcerted to find that I'm getting stack overflows for more
than two thousand iterations of my recursive function.
This is a problem. As it stands, my program (below) is unable to price a
convertible bond with more than about a year to maturity.
Is there some way round this? Perhaps I should be implementing the iteration
in some other way?
Alistair
NAS=: 100
dS=: 2
S=: dS*i.NAS
k=: 135
r=: 0.05
b=: 113.22
dL=: %365
sigma=: 0.4
dt=: 0.9%*:sigma*NAS
Sgtk=: S#~S>k
Sltk=: S#~S<:k
Delta=: (2*dS)%~2&}.-_2&}.
Gamma=: (*:dS)%~2&}.+_2&}.-2*}.@:}:
dV_dL=: dL%~}."_1-}:"_1
negTheta_ltk=:
([:-r*{.@:[),(((r*}.Sltk)*Delta)+(0.5**:sigma*}.Sltk)*Gamma)@:([,{.@:{.@:])-r*}.@:[
step_gtk=:
((}:@:]+dt*(((r*}:Sgtk)*Delta)+(0.5**:sigma*}:Sgtk)*Gamma)@:({:@:[,])-r*}:@:])(}:"_1@:]))+(dt*dV_dL@:}:@:])
V_ltk=: Sltk>.[+dt*negTheta_ltk
V_gtk=: (Sgtk>.b,.~],({.-~2*{:)@:(_2&{.))@:step_gtk
Vrec=: (>@:{.(V_ltk;V_gtk)>@:{:)@:V@:<:
V=: Vrec`((b$~+/S<:k);(b$~16,~+/S>k)"0)@.(0=])
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