Ho-Lee and Hull-White Extended Vasicek/CIR: Derivation of the Drifts using HJM

[@minhle9868]

Man, my lectures on these subjects are ridiculously difficult to understand. You are doing us a huge favor!! Thanks so much, subscribed! Keep up the awesome work!

[@quantpie]

Glad to hear that! Many thanks!!

[@quantpie]

For alternative derivation of drift, please see: Hull White Extended Vasicek: quantpie.co.uk/srm/hull_white_sr.php Ho-Lee: quantpie.co.uk/srm/ho_lee_sr.php

[@dafdaf4052]

Excellent. Could you also indicate the source code for Hull White Short Rate model (One Factor) in your website; I am curious how you implemented it.

[@quantpie]

Thanks! Noted, shall do, but need to extract the code from library, so will need a bit of testing!

[@dafdaf4052]

@@quantpie Thank you, seriously, as a quant student these videos are one of the best sources online for understanding the intuition behind the topics. I am certain the channel will grow rapidly relative to this small community :*)

[@luzianlechner1884]

perfectly explained!

[@liangguo8393]

Great lecture. The derivation for CIR model is quite difficult. Could we have the demonstration or at least the expression of the \sigma_f(t,T) and \theta_t to check if we get the right answer ? Thanks a lot.

[@zhiyanghan2816]

Could you please show the process of CIR? It is really hard to compute....

[@quantpie]

hello! You mean how to implement it? many thanks for the question!

[@zhiyanghan2816]

​@@quantpie Yes! I use Matlab to find the differential part, it is really a complex computation.

[@quantpie]

@@zhiyanghan2816 You can find the derivation of the short rate/zero coupon bonds formulae here: quantpie.co.uk/srm/cir_sr.php

[@prasadkamath1205]

Hello great videos! loved it! I am new to this short rate modelling and trying to value ZC bond using CIR. my confusion is around calibration of the parameters, how do we get the mean reversion spead, mean and the initial value of short rate r. Do you have anything on that?

[@quantpie]

Many thanks for the question! There are two broad ways to calibrate the model: 1) using historical short rate data, which we have covered for a slightly different process, OU process, the approach for CIR would be similar, though the regression equation/details will be different. 2) using the current zero coupon prices (yield curve), you try to find the parameters so that the model prices match the market prices of the zero coupon prices- essentially boils down to optimisation/root finding. In the extended CIR this happens by construction! You can also mix and match - estimate some parameters, say mean reversion, using historical data, and the rest using market prices.

[@prasadkamath1205]

@@quantpie thanks again, that was helpful

[@EricHH122]

Any plan to publish these lectures as a book? It would be a best seller. I am writing notes for each lecture and I got a thick notebook filled. Writing notes helps me to understand what is going on better.

[@quantpie]

We are planning to add the notes to the website, but progress has been slower because get distracted by new videos!!