Andrija Djurovic on LinkedIn: The_Vasicek_Distribution_App (2024)

𝐓𝐡𝐞 𝐕𝐚𝐬𝐢𝐜𝐞𝐤 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧The 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.

310

3 Comments

𝐁𝐨𝐨𝐭𝐬𝐭𝐫𝐚𝐩 𝐇𝐲𝐩𝐨𝐭𝐡𝐞𝐬𝐢𝐬 𝐓𝐞𝐬𝐭𝐬 𝐢𝐧 𝐂𝐫𝐞𝐝𝐢𝐭 𝐑𝐢𝐬𝐤Bootstrapping finds application in various domains of credit risk modeling, but it is especially beneficial in hypothesis testing when there is no consensus on the estimates' standard error, or the testing procedure is absent. In this context, bootstrapping demands special attention, particularly when practitioners aim to calculate the p-value, as it does not produce data conforming to the null hypothesis.Check out my new presentation, showcasing one of the frequently utilized approaches and metrics for validating credit risk models.The GitHub page is available via the link in the comment section.

255

3 Comments

𝐋𝐢𝐤𝐞𝐥𝐢𝐡𝐨𝐨𝐝 𝐀𝐩𝐩𝐫𝐨𝐚𝐜𝐡𝐞𝐬 𝐭𝐨 𝐋𝐨𝐰 𝐃𝐞𝐟𝐚𝐮𝐥𝐭 𝐏𝐨𝐫𝐭𝐟𝐨𝐥𝐢𝐨𝐬One method for estimating the PD for Low Default Portfolios (LDP) is Alan Forrest's likelihood approach. His proposal to switch from the probability of the class of data outcome (as presented in the Pluto-Tasche or BCR papers) to the likelihood and likelihood ratio is crucial as it establishes a direct connection with the classical theory of statistical inference and its well-known approximations, which are also valid for high default cases. I extended the above framework to the portfolio-level multi-year period design, which is often considered a prevalent method in PD estimation. In essence, I introduced year-to-year correlation in the simulation of systemic factors, leading to a change in the calculation of expected likelihood from the proposed analytical approach to Monte Carlo simulation.Check out my new presentation for detailed information on the proposed adjustment. Additionally, I will consider incorporating the adjusted approach into one of the new versions of my 𝐏𝐃𝐭𝐨𝐨𝐥𝐤𝐢𝐭 R package.Lastly, I want to thank Alan Forrest for his comments and motivating feedback, which encouraged me to continue working in this field.

185

7 Comments

𝐋𝐨𝐰 𝐃𝐞𝐟𝐚𝐮𝐥𝐭 𝐏𝐨𝐫𝐭𝐟𝐨𝐥𝐢𝐨𝐬 - 𝐂𝐨𝐧𝐬𝐞𝐫𝐯𝐚𝐭𝐢𝐯𝐞 𝐄𝐬𝐭𝐢𝐦𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐃𝐞𝐟𝐚𝐮𝐥𝐭 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐢𝐞𝐬Estimating the Probability of Default (PD) for low default portfolios typically poses a significant challenge for practitioners. The scarcity of defaults undermines PD estimates' reliability and statistical validity based on historical default experience. This issue is also a primary concern for regulators, given that PD based solely on simple historical averages or judgmental considerations may underestimate the bank's capital requirements.My latest presentation illustrates the Benjamin-Cathcart-Ryan approach for conservative PD estimation in low default portfolios. The presented simulation focuses on a prevalent design in practice: multi-year period estimation, which considers asset and year-to-year correlation. However, other methods are also utilized for this purpose. I encourage readers and practitioners to explore other approaches, and I will showcase some of them in one of the upcoming posts.The accompanying files for the presentation are on my GitHub page (link in the comment).

471

29 Comments

𝐒𝐭𝐚𝐭𝐢𝐬𝐭𝐢𝐜𝐚𝐥 𝐛𝐢𝐧𝐧𝐢𝐧𝐠 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐢𝐜 𝐫𝐢𝐬𝐤 𝐟𝐚𝐜𝐭𝐨𝐫𝐬While binning is not a mandatory step in developing credit risk models, practitioners commonly employ it because it offers some advantages over using continuous risk factors. With time, certain principles have emerged as the best practices in the binning process.Different software offer diverse solutions for the binning process. I have authored several packages specifically designed for this purpose, such as monobin, monobinShiny, and PDtoolkit in R and monobinpy in Python. These packages encompass the most frequently employed methods I have encountered in credit risk practice. I always encourage readers and users to explore and compare different options as alternative packages are available.Check out my latest presentation for basic insights into the binning process.

217

11 Comments

𝐌𝐞𝐚𝐬𝐮𝐫𝐢𝐧𝐠 𝐂𝐨𝐧𝐜𝐞𝐧𝐭𝐫𝐚𝐭𝐢𝐨𝐧 𝐑𝐢𝐬𝐤Concentration risk represents a significant source of risk in banking, particularly in emerging and small economies. Banks are required to independently assess and allocate capital buffers to mitigate concentration risk as part of Pillar 2 models. Quantifying this type of risk often presents significant challenges to the modelers.Check out my new presentation, which demonstrates a partial portfolio approach as a solution to address concentration risk.

302

8 Comments

𝐄𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞The effective interest rate is a commonly employed financial term in the domain of loans, signifying the genuine expense of borrowing for a borrower over a specified period. It encompasses the nominal interest rate and additional fees and charges associated with the loan. The attached example demonstrates calculating the effective interest rate using R and Python, assuming the overall loan cost is deducted from the initially approved amount. While real-world scenarios may differ, this example can serve as a solid basis for adjusting to specific cases.The link to a GitHub page containing the same example is available in the comment section.

86

2 Comments