# What is a good Computer Algebra System for financial engineering?

I would like to know if there exists some computer algebra systems adapted to calculate pricing based on particular models, i.e. pricing YoY Inflation Swap under Jarrow Yildirim Model.

I know that the results are known and showed in books such as Brigo & Mercurio, but I would like to be able to reproduce the results using some code in order to avoid stupid typos in mathematical passages.

• High Mitch76, it's a good question but it would benefit from having embedded links to some reference page for the model and the book you're referring to. – SRKX Oct 15 '14 at 9:26
• Hi @SRKX thanks for your suggestion, actually I'm looking for a generic framework but you're right, adding a particular model helps casting the problem. The model I'm trying to reproduce is Jarrow Yildirim Model, which ca be seen at fabiomercurio.it/Inflation.pdf – Mitch76 Oct 15 '14 at 12:25

## 1 Answer

I am rather a fan of mathematical/statistical software for doing numerical finance (R/Matlab).

But returning to your question: The commercial software UNRISK is based on mathematica, a computer algebra system.

Usually you can use the Unrisk functions right in mathematica and price financial derivatives there. There also exists Jave interfaces if you want to use these functions outside of mathematica.

• I don't know Unrisk but I think in mathematica it's hard to solve stochastic differential equations (SDEs). It might help during some computation steps though. – SRKX Oct 16 '14 at 1:05
• The OP asked for computer algebra (although I always wonder why people would use such systems for these things) and as far as I know mathematica together with UNRISK (not without it) is the only such combination. You need to use unrisk then adapted integration for various derivatives and models is implemented. I know they even have IL derivatives there ... – Ric Oct 16 '14 at 6:51
• That's exactly my problem. When doing calculation you have huge terms that are purely algebraic, and finally you have to take some expectation values. I would love a computer algebra framework which prevents me from doing naive error in algebra simplifications and symbolic integration and at the same time able to perform mean and variances of stochastic processes. – Mitch76 Oct 17 '14 at 10:59
• mathematica can do symbolic algebra and a integration (it know a lot of special functions (Bessel and this kind). And you can do numerics too. So this could be a place to start. – Ric Oct 17 '14 at 11:20