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

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Derives the drift function of Ho-Lee and Hull-White Extended Vasicek using HJM framework. Include the Hull White extended CIR as an exercise, which you should be able to derive easily once you understand the idea. Here is the outline of the content by timeline:
0:32/15:01: A quick recap of the Merton, Vasicek, and CIR dynamics
3:56/15:01: Explain the purpose of the extended versions
6:00/15:01: Derive the connection between the dynamics of the instantaneous forward and the short rate
07:54/15:01: Shows how to express the three short rate models in the HJM form
09:13/15:01: Use the HJM form of the Merton model to infer the drift of the Ho Lee model
11:13/15:01: Use the HJM form of the Vasicek model to infer the drift of the Hull White extended model
14:31/15:01: Outline the exercise to do the same for the CRR

Опубликовано:

25 май 2019

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Комментарии : 17

@minhle9868 4 года назад

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 4 года назад

Glad to hear that! Many thanks!!

@luzianlechner1884 Год назад

perfectly explained!

@quantpie 5 лет назад

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

@prasadkamath1205 3 года назад

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 3 года назад

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 3 года назад

@@quantpie thanks again, that was helpful

@liangguo8393 9 месяцев назад

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.

@dafdaf4052 4 года назад

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 4 года назад

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

@dafdaf4052 4 года назад

@@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 :*)

@EricHH122 3 года назад

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 3 года назад

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