Andrija Djurovic on LinkedIn: The_Vasicek_Distribution_App (2024)

Andrija Djurovic

Senior Manager, Risk Advisory - Central Europe at Deloitte

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๐„๐ฌ๐ญ๐ข๐ฆ๐š๐ญ๐ข๐ง๐  ๐ญ๐ก๐ž ๐๐š๐ซ๐š๐ฆ๐ž๐ญ๐ž๐ซ๐ฌ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐•๐š๐ฌ๐ข๐œ๐ž๐ค ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐จ๐งAs a follow-up to my previous post about the Vasicek distribution, I built a small Shiny application to fit the distribution to observed default rates. The application allows users to choose specific estimation methods and compare results. This can be done with a provided dummy dataset or by uploading a particular dataset following the instructions on the application's landing page.Those interested can check out the app via the link in the comments section.In the upcoming posts, I'll compare the biases of different estimation methods and explore potential modifications to the underlying distribution of the Vasicek model.

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Andrija Djurovic

Senior Manager, Risk Advisory - Central Europe at Deloitte

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Shiny app:https://andrijadj.shinyapps.io/vasicek_distribution/The Vasicek Distribution post:

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Alan Forrest

Model Risk Professional

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Andrija - Good post and excellent insights. Definitely the Vasicek model is the entry point to the deeper understanding of portfolio-level default behaviour, and \rho is the critical ingredient. Your calculations show the correct way to use and estimate \rho from data at hand.However, a word of caution. My experience here is that the value of \rho is statistically extremely uncertain if estimated only from internal data available to a financial institution- the likelihoods have very flat maxima. Even large portfolios (say 10^7 obligor years) and reasonably long time series (say 10 years) produce 90% confidence intervals for \rho (say for mortgages) that span almost 2 orders of magnitude. And if you want to vary \rho across risk bands (as is expected intuitively), then that is yet another noisy complication. I think this statistical uncertainty and the necessity of market-scale (not bank-scale) data, were behind the regulator's decision to prescribe particular values or formulae for \rho in the Basel 2 Accord. However in economic capital modelling and elsewhere there remains the need to appreciate the uncertainty of \rho, and I saw this uncertainly routinely underestimated whenever such models crossed my desk for validation.

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Marc Labat, CFA

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Thanks for sharing

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Andrija Djurovic on LinkedIn: The_Vasicek_Distribution_App (40)

Andrija Djurovic on LinkedIn: The_Vasicek_Distribution_App (41)

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