Vasicek Model Vs Cox Ingersoll Ross (CIR) Model (FRM Part 2, Book 1, Market Risk)

In this video from the FRM Part 2 curriculum, we take a comparative look at two one factor short term interest rate models: the Vasicek Model and the Cox Ingersoll Ross (CIR) Model. We compare these models along the following lines or aspects:
1) Category: Arbitrage Free vs Equilibrium
2) Mean Reversion
3) Basis Point Volatility
4) Negative Rates
5) Terminal Distribution
6) Prices of OTM Options
7) Mathematical Tractability
For more videos on FRM Part 2 preparations, please visit the course page: www.finRGB.com....

[@finRGB]

FRM Learning Objectives:
1) Describe the effectiveness of the Vasicek Model.
2) Describe the short-term rate process under the Cox-Ingersoll-Ross (CIR) and lognormal models.
3) Calculate the short-term rate change and describe the basis point volatility using the CIR and lognormal models.

[@austinchi8138]

Just want to say your videos are by far the best I've come across with regards to FRM concepts, they are so well explained and illustrated and helped me understand many concepts that I wasn't able to grasp the ideas of! Thank you for posting these videos!

[@finRGB]

Thank you for the kind words of appreciation, Austin.

[@louroth5282]

Thank you so much! This was very informative and easy to follow, whilst to the point. Taught me exactly what I was looking to learn.

[@haythemtilouch1191]

Question : what's the diffrence between vasicek for credit risk capital and this vasicek ?
Btw your the only one who explain's advanced concepts with simple words in youtube thank you so much.

[@finRGB]

Thank you for the appreciation.
This Vasicek model is an interest rate model i.e. provides a possible means of evolution of the "short rate" over time. The Vasicek model for credit risk capital makes use of the Gaussian copula and one factor model to arrive at the loss distribution for a portfolio of loans / credits. From the loss distribution, an extreme loss can be read and credit risk capital computed. The video for this model is available here: th-cam.com/video/t9OOTbyOWhs/w-d-xo.htmlfeature=shared

[@francoiscoetzer9920]

Fantastic video, thank you.

[@finRGB]

Thank you for the appreciation, Francois.

[@mangzl338]

how do you constructs the graph? If you can share, that will help me a lot. Thank you

[@finRGB]

Hello Mangz L, the graphs were constructed using a simple Monte Carlo simulation of short term interest rate (in Excel). The model parameters were k=0.25, theta = 0.06, sigma = 0.02 for Vasicek and sigma = 0.082 for CIR. For comparison sake, paths of the same color share the same shocks.

[@dhruvrathore1011]

Very informative video

[@finRGB]

Glad you found the video useful, Dhruv.

[@anindyakundu8420]

It is extremely useful... Can you please make a similar video on no arbitrage (Hull White) vs Equilibrium (Vasicek) model?

[@finRGB]

Thank you, Anindya. Will do.

[@bryanjimenez9745]

Model cir has a analitic solution? Why?