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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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1 Answer 1

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:

http://belkcollegeofbusiness.uncc.edu/wtian1/bdt.pdf

http://www.csie.ntu.edu.tw/~lyuu/finance1/2012/20120530.pdf

http://www.iam.fmph.uniba.sk/studium/efm/phd/urbanova/urbanova-thesis.pdf

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My question was how to select appropriate parameters for BDT in order to simulate it with Monte-Carlo. I am trying to avoid trees (as suggested by papers 1 and 2). And the third paper is too general and tells nothing about calibration –  Rustam Jan 17 '13 at 13:34
    
added several papers that show detailed steps in how to calibrate the BDT model. It is a calibration process there are no magic parameters that you plug in and voila your model is calibrated –  Matt Wolf Jan 17 '13 at 15:59

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