Andrija Djurovic on LinkedIn: The_Vasicek_Distribution (2024)

Andrija Djurovic

Senior Manager, Risk Advisory - Central Europe at Deloitte

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๐“๐ก๐ž ๐•๐š๐ฌ๐ข๐œ๐ž๐ค ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐จ๐งThe Vasicek Distribution holds a special place in credit risk modeling, finding applications in various areas including, but not limited to, IRB modeling, capital requirement calculations, IFRS9 modeling, and measuring concentration risk. Like other statistical distributions, the Vasicek distribution follows a specific functional form with parameters requiring estimation.Check out my new presentation, which briefly introduces the Vasicek distribution.In addition to this presentation, I am preparing to publish a Shiny application dedicated to fitting the parameters of the Vasicek distribution to observed data. Those interested can follow the GitHub link in the comments section to stay updated on upcoming announcements.

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Andrija Djurovic

Senior Manager, Risk Advisory - Central Europe at Deloitte

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Shakeel I.

Performance Analytics

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Banks apply the Vasicek model for credit risk in the IRB approach. The Probability Density Function in Slide 3 (of Andrija Djurovicโ€™s excellent presentation) is important to Banks. For estimating parameters, a particular case of the maximum likelihood method (Slide 4) is the ASRF model. The ASRF model's parameters can also be estimated using probit-linear regression.BASEL adopted the assumptions of a normal distribution for the systematic and idiosyncratic risk factors. While IFRS9 focuses on Expected Loss (EL) for provisioning, BASEL capital requirement is taken to be the contribution of an exposure to the Unexpected Loss (UL). For BASEL, the regulator prescribes the asset correlation (asset class-wise).Under some constraints (single systematic risk factor, infinite number of small loans, dependence among obligors), Mertonโ€™s model protracts to the ASRF model. Vasicek used the standard geometric Brownian motion model, providing an analytical solution to model loss distribution. The result is a โ€œStylized Loss Distributionโ€ which visualizes some essential metrics for a Bankโ€™s capital requirement calculations as follows:Unexpected Loss (i.e. ASRF Capital) = Value-at-Risk @ 99.9% โ€“ Expected LossExcellent post!

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Andrija Djurovic on LinkedIn: The_Vasicek_Distribution (29)

Andrija Djurovic on LinkedIn: The_Vasicek_Distribution (30)

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