Books/Materials about Term Structure Payoffs implementation

Hi Community,

Many C++ quantitative books use relatively simple payoffs (e.g. European, America , Barrier options) as examples to illustrate the design of the pricing application. These products’ payoff are pretty easy to implement in MC’s terminal or PDE’s initial condition.

However, the OTC market trades more complex payoffs which involves term structure (e.g. cap/floor, IRS callable, Accumulator, Target forward resumption). And it is not straight-forward in terms of how to integrate their payoff into the pricing engine (MC or PDE).

In practice, I have some questions:
(1) how would you design the Payoff case to make it a term-structure like?
(2) how would you adapt the MC or PDE pricing engine’s input and conditions to be able to price term-structure-like products?
(3) is there any books/resources/code samples to give us an idea of the application design?

Daniel Duffy

C++ author, trainer
Well, first there are not many books in C++ for quant finance (most authors of finance books don't know/do C++). Second, PDE methods have traditionally been for equities although they can and have been applied to fixed income (CIR, Hull White), convertible bonds and such-like. Some chapters are in my 2022 PDE book.

No silver bullet. No quick fix.
Plan B Build your own software system. Need knowledge of finance, PDE, C++. And coaching.
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Daniel Duffy

C++ author, trainer
Just out of curiosity, is your question from a personal (student) perspective or for production software?
Just out of curiosity, is your question from a personal (student) perspective or for production software?
Thanks Professor.
The question is more for production software.
I understand that for more complex payoffs we might need to use MC instead of PDE.

One specific example: if I need to price a Bermudian Swaption, whose payoff involves multiple exercise dates, with Monte Carlo.
We will expect to add the exercise dates into the MC’s diffusion time steps also.

But how would C++ quant practitioners design:
(1) the framework of the payoff class to be able to represent different kinds of term-structure payoffs (e.g. Berm Swaption, Cap/Floor and IRS Callable);
(2) the MC engine to be generalized enough to use any un-uniform time mesh and smart enough to check exercise on exercise dates.

Daniel Duffy

C++ author, trainer
What research have you done into this? Or is it brainstorming at this stage? Your question is kinda general.

Why not purchase a commercial package?

for swaptions, see "C# in Financial Markets" by Duffy and Germani (Wiley, 2013)
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