Convertible Bond Pricer with AFV model

[Ryan Shrott]

Anyone experienced with pricing convertible bonds as in this paper: https://cs.uwaterloo.ca/~paforsyt/convert.pdf ? I'm looking at implementing the model. Any words of wisdom?

 

[Daniel Duffy]

Ryan,
That's a nice challenging project Are you doing it by FDM?

A quick glance is that it is a system of PDEs with constraints, more or less?

Some approaches

1. Method of Line (MOL) with penalty/barrier using Boost C++ odeint.
Chapter 1. Boost.Numeric.Odeint - 1.67.0

(basically, you discretize in S only and let the solver do the t part, cool, yes?)

2. ADE method.
https://onlinelibrary.wiley.com/doi/epdf/10.1002/wilm.10366
https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118818572.app3
https://www.wilmott.com/wp-content/uploads/2016/07/160718_ade.pdf

Both 1 and 2 are easy to program.

3. Crank Nicolson etc. of course.

 

[Ryan Shrott]

@Daniel Duffy Yes, FDM. I want to implement the model in this paper: https://cs.uwaterloo.ca/~paforsyt/convert.pdf

 

[Daniel Duffy]

I would say go for it and come back when you have questions. Good luck
In this case the journey might be as important as the destination.

It's a good example. It's always good to have at least 2 solutions, just in case.

Have you requirement like speed, accuracy etc. ?

https://wwwf.imperial.ac.uk/~ajacquie/IC_Num_Methods/IC_Num_Methods_Docs/Literature/DuffyCN.pdf

 

[Ryan Shrott]

Thanks for the help. I will let you know how it goes.

 

[Daniel Duffy]

You're welcome. One of my MSc students has done a HW2 Bermudan callable bond project using ADE (I did the MOL part) and will probably do a convertible bond in ADE soon.
It would be good to keep in touch.