# BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$.

I assume I already have steady-state IR curve $r^*(t)$ and volatility curve $\sigma^*(t)$.

It makes no difference whether it would be binomial tree or Monte-Carlo or FDM implementation. Monte-Carlo seems to be easy but I'm not sure whether I can use $\theta(t) = r^*(t)$ and $\sigma(t)=\sigma^*(t)$.

I went thru Derman's article and Haug's "Options pricing formulas" but found no answer.

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All you need is to use the discretization to implement the MC approach. The following links should get you started:

http://www.lcy.net/files/BDT_Seminar_Paper.pdf

http://www-2.rotman.utoronto.ca/~hull/TechnicalNotes/TechnicalNote23.pdf

http://www.iorcf.unisg.ch/Forschung/~/media/Internet/Content/Dateien/InstituteUndCenters/IORCF/Abschlussarbeiten/Frey%202008%20MA%20Monte%20Carlo%20methods%20with%20application%20to%20the%20pricing%20of%20interest%20rate%20derivatives.ashx

In the last paper check from section 6.2

The following papers show examples of BDT model calibration: