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This is my first time posting a question. I have very limited experience in the field of stochastic calculus and interest rate modelling. I have been tasked with implementing the short rate model introduced in Jamshidian and Zhu (1997) for the purpose of estimating stressed interest rates for interest rate risk in the banking book. The model is specified as follows:

enter image description here

In effect it is a log normal short rate model that has a standard Ornstein Uhlenbeck process as the stochastic driver. The model also includes PCA of the yield curve hence the beta weights on the Y_k terms in the discretized version of the model which is specified as:

enter image description here

My question is how do I get this solution? I have no idea of how to solve the SDEs so that I end up with the discretized version shown above. I include a link to the original paper by Jamshidian and Zhu.

http://www.ime.usp.br/~rvicente/risco/jamshidian.pdf

Reference to the short rate model are made on p3 and p9. I hope that I have stated the question clearly. Any help would be greatly appreciated because I am about to pull my hair out.

Thanks

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Why don't you use the Monte-Carlo method suggested in the paper ? Essentially u need a joint distribution of the discount factor and the short rate model. For details related to Vasicek you may check Glasserman's textbook

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