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Expected loss is a key risk measure for loan pricing and capital allocation for regulatory purposes. Expected loss rate measures the expected loss for one dollar exposure. Under current regulatory model framework, this rate is calculated as LGD multiplied by PD. The rate may have been underestimated for accounts with high PD, when LGD is strongly correlated with PD. It may also have been overestimated for accounts with low PD, an issue due to the sample bias in LGD model development, which skews heavily towards the high PD end. Approaches commonly used in the industry for addressing PD and LGD correlation involve a splitting of risk into two parts: systematic and idiosyncratic, under the asymptotic single factor risk (ASFR) model framework. The correlation between two systematic factors for PD and LGD is estimated and used for impact analysis. Adjustments are then taken. In this paper, we propose an approach to directly minimizing estimation biases. A correction is done to the existing LGD model by adding a hidden factor, from the existing PD model side, structured like a simple neural network. Under this model framework, parameters for existing LGD drivers and the hidden factor are trained and updated by a machine learning algorithm, to minimizing estimation biases. Experiments show, this model framework is robust, it provides an effective tool for fixing these bias issues. Keywords: Expected Loss, Pd and LGD Correlation, Cost Function, Stochastic Gradient, Gradient Descent, Neural Network Cite this Article: Bill Huajian Yang, Estimating Expected Loss Rate in Presence of PD and LGD Correlation, International Journal of Artificial Intelligence & Machine Learning (IJAIML), 2(1), 2023, pp. 65-74.

This paper develops a Cournot model to study how environmental regulatory policies affect the international competitiveness of firms. The tradable baseline-and-credit emission permit is employed as the primary means of environmental regulation. It provides a theoretical support for the government environmental regulatory policies. - Questo studio sviluppa un modello di Cournot per analizzare come le politiche di regolamentazione ambientale influenzino la competitività internazionale delle imprese. Il sistema dei diritti di emissione negoziabili viene impiegato come principale mezzo di regolamentazione ambientale e si fornisce un supporto teorico per l’applicazione di tali regolamentazioni.

The Tax Reform Act of 1986 (TRA) has sometimes been portrayed as a genuine effort to introduce fairness, simplicity, and economic growth considerations into the Internal Revenue Code of the U.S. Although regarding the TRA as far from adequate, the late Richard Musgrave did in fact regard this statute as yielding many significant changes that improved the equity and efficiency of the process of federal income taxation. The present study investigates empirically whether the TRA was so well received by taxpayers as to increase (at least in theory) the degree of federal personal income tax compliance. Although the estimates imply that this may have initially been the case, a more in-depth analysis reveals that the TRA actually exercised a statistically zero net impact on the aggregate degree of personal income tax compliance over the longer run, implying that the TRA merely required a sufficient amount of time for tax evaders to learn the new law so that they could ultimately resume their tax-evasion ways.

Hereditary angioedema (HAE) is a disease which is associated with random and often unpredictable attacks of painful swelling typically affecting the extremities, bowel mucosa, genitals, face and upper airway. Attacks are associated with significant functional impairment, decreased Health Related Quality of Life, and mortality in the case of laryngeal attacks. Caring for patients with HAE can be challenging due to the complexity of this disease. The care of patients with HAE in Canada is neither optimal nor uniform across the country. It lags behind other countries where there are more organized models for HAE management, and where additional therapeutic options are licensed and available for use. The objective of this guideline is to provide graded recommendations for the management of patients in Canada with HAE. This includes the treatment of attacks, short-term prophylaxis, long-term prophylaxis, and recommendations for self-administration, individualized therapy, quality of life, and comprehensive care. It is anticipated that by providing this guideline to caregivers, policy makers, patients and their advocates, that there will be an improved understanding of the current recommendations regarding management of HAE and the factors that need to be considered when choosing therapies and treatment plans for individual patients. The primary target users of this guideline are healthcare providers who are managing patients with HAE. Other healthcare providers who may use this guideline are emergency physicians, gastroenterologists, dentists and otolaryngologists, who will encounter patients with HAE and need to be aware of this condition. Hospital administrators, insurers and policy makers may also find this guideline helpful.

Systematic risk has been a focus for stress testing and risk capital assessment. Under the Vasicek asymptotic single risk factor model framework, entity default risk for a risk homogeneous portfolio divides into two parts: systematic and entity specific. While entity specific risk can be modelled by a probit or logistic model using a relatively short period of portfolio historical data, modeling of systematic risk is more challenging. In practice, most default risk models do not fully or dynamically capture systematic risk. In this paper, we propose an approach to modeling systematic and entity specific risks by parts and then aggregating together analytically. Systematic risk is quantified and modelled by a multifactor Vasicek model with a latent residual, a factor accounting for default contagion and feedback effects. The asymptotic maximum likelihood approach for parameter estimation for this model is equivalent to least squares linear regression. Conditional entity PDs for scenario tests and through-the-cycle entity PD all have analytical solutions. For validation, we model the point-in-time entity PD for a commercial portfolio, and stress the portfolio default risk by shocking the systematic risk factors. Rating migration and portfolio loss are assessed.

In this paper, we propose a Vasicek-type of models for estimating portfolio level probability of default (PD). With these Vasicek models, asset correlation and long-run PD for a risk homogenous portfolio both have analytical solutions, longer external time series for market and macroeconomic variables can be included, and the traditional asymptotic maximum likelihood approach can be shown to be equivalent to least square regression, which greatly simplifies parameter estimation. The analytical formula for long-run PD, for example, explicitly quantifies the contribution of uncertainty to an increase of long-run PD. We recommend the bootstrap approach to addressing the serial correlation issue for a time series sample. To validate the proposed models, we estimate the asset correlations for 13 industry sectors using corporate annual default rates from S&P for years 1981-2011, and long-run PD and asset correlation for a US commercial portfolio, using US delinquent rate for commercial and industry loans from US Federal Reserve.

The Basel Accords have created the need to develop and implement models for PD, LGD and EAD. Although PD is quite well researched, LGD and EAD still lag both in theoretical and practical aspects. This paper proposes some empirical approaches for EAD/LGD modelling and provides technical insights into their implementation. It is expected that modellers will be able to use the tools proposed in this paper.

This theoretical note elaborates upon why it is a myth that YTM is viewed as only a promised but not really earned interest rate. It addresses some misconceptions in Shirnani and Wilbratte (2009) on what, between YTM and RCY, is a true rate of return of a coupon bond, why YTM is not just a "fictitious mathematical construct," and why YTM has nothing to do with a yield curve.

This note comments on a misconception that yield to maturity from holding a coupon bond until maturity is only promised, but not really received, unless coupon payments are reinvested at the same rate as the (original) yield to maturity. It shows that yield to maturity is always earned no matter how coupon payments are allocated, i.e., whether spent or reinvested at any rate. It illuminates that the realized compounding yield in fact measures the yield to maturity from a combination of two investments rather from simply holding the bond itself until maturity.