FixedIncomeRisk Forum

professor, i need some help in programming the non-central chi square density for solving an option price under CIR. Whats the best way to do this? Are there ready progrms that can do this?

Bond_girl,

Yes, you can find some programs that will help you to compute the non-central chi square distribution function on the net. However, you might find convergence problems and crashes because the approximations of Chi are somewhat problematic.

We worked on this issue for our second book “Dynamic Term Structure Model” (Wiley 2007 – Nawalkha, Soto and Beliaeva) and we can give you an Excel file including the code for the non-central chi square that works for nearly all cases. It uses the function implemented in Excel for the central chi squared (non-centrality parameter =0) and two routines for the non-central chi-squared. That way, if one fails, the other is used. I hope it helps.

Also note that CIR type options can be also solved using the Fourier method (for options on zero-coupon bonds) and the cumulant expansion method (for options on coupon bonds). You can find a discussion of these methods in chapters 5 and 9 of our book. For multifactor models these are the only approaches that will let you to get a solution for the option price.

I encourage you to use the software for Single and Multifactor Affine Term Structure Models we provide with the book for testing your work and also explore single and multifactor CIR type models for pricing bonds and derivatives. You can download the software from fixedincomerisk.com website.

Best regards,
Gloria