Fast Simulation of Multifactor Portfolio Credit Risk

We consider the problem of decomposing the credit risk in a portfolio into a sum of risk contributions associated with individual obligors or transactions. For some standard measures of risk – including value-at-risk and expected shortfall – the total risk can be usefully decomposed into a sum of marginal risk contributions from individual obligors. Each marginal risk contribution is the conditional expected loss from that obligor, conditional on a large loss for the full portfolio. We develop methods for calculating or approximating these conditional expectations. Ordinary Monte Carlo estimation is impractical for this problem because the conditional expectations defining the marginal risk contributions are conditioned on rare events. We develop three techniques to address this difficulty. First, we develop importance sampling estimators specifically designed for conditioning on large losses. Next, we use the analysis underlying the importance sampling technique to develop a hybrid method that combines an approximation with Monte Carlo. Finally, we take this approach a step further and develop a rough but fast approximation that dispenses entirely with Monte Carlo. We develop these methods in the Gaussian copula framework and illustrate their performance in multifactor models.

Demand for sustainable fixed-income investment solutions is surging but there is hardly research on the impact of sustainability on the risk characteristics of fixed-income portfolios. This study examines the impact of sustainability on the credit risk exposure of corporate bond portfolios between 2013 and 2020 by analyzing the returns of sustainable and non-sustainable portfolios using two different asset pricing models and environmental, social, and governance (ESG) ratings from different providers. Controlling for a set of portfolio characteristics, our results show that sustainable portfolios are significantly less exposed to credit risk than their non-sustainable peer portfolios. This finding implies that considering ESG criteria in portfolio management is a suitable means to systematically manage credit risk. Being the first study to investigate the relationship between sustainability and credit risk on a portfolio level, this study contributes to the understanding of the effects of ESG criteria in portfolio management and provides academics and investment professionals with valuable insights.

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The accurate measurement of credit risk can be modeled as a rare event simulation problem. While Monte Carlo simulation is time-consuming for rare events, importance sampling techniques can effectively reduce the simulation time, thus improving simulation efficiency. This chapter proposes a new importance sampling method to estimate rare event probability in simulation models. The optimal importance sampling distributions are derived in terms of expectation in the normal copula model developed in finance. In the normal copula model, dependency is introduced through a set of common factors of multiple obligors. The intriguing dependence between defaults of multiple obligors imposes hurdles in simulation. The simulated results demonstrate the effectiveness of the proposed approach to solving the portfolio credit risk problem.

Standard market risk optimization tools, based on assumptions of normality, are ineffective for evaluating credit risk. In this article, the authors develop three scenario optimization models for portfolio credit risk. They first create the trading risk profile and find the best hedge position for a single asset or obligor. The second model adjusts all positions simultaneously to minimize the regret of the portfolio subject to general linear restrictions. Finally, a credit risk‐return efficient frontier is constructed using parametric programming. While scenario optimization of quantile‐based credit risk measures leads to problems that are not generally tractable, regret is a relevant and tractable measure that can be optimized using linear programming. The three models are applied to optimizing the risk‐return profile of a portfolio of emerging market bonds.

Chapter 11 - Estimating Parameters Required for Credit Risk Modeling

Parameterizing Credit Risk Models

In this paper we use a reduced form model for the analysis of Portfolio Credit Risk. For this purpose, we fit a Dynamic Factor model, DF, to a large dataset of default rates proxies and macro-variables for Italy. Multi step ahead density and probability forecasts are obtained by employing both the direct and indirect method of prediction together with stochastic simulation of the DF model. We, first, find that the direct method is the best performer regarding the out of sample projection of financial distressful events. In a second stage of the analysis, the direct method of forecasting through principal components is shown to provide the least sensitive measures of Portfolio Credit Risk to various multifactor model specifications. Finally, the simulation results suggest that the benefits in terms of credit risk diversification tend to diminish with an increasing number of factors, especially when using the indirect method of forecasting.

Credit risk assessment is at the core of modern economies. Traditionally, it is measured by statistical methods and manual auditing. Recent advances in financial artificial intelligence stemmed from a new wave of machine learning (ML)-driven credit risk models that gained tremendous attention from both industry and academia. In this paper, we systematically review a series of major research contributions (76 papers) over the past eight years using statistical, machine learning and deep learning techniques to address the problems of credit risk. Specifically, we propose a novel classification methodology for ML-driven credit risk algorithms and their performance ranking using public datasets. We further discuss the challenges including data imbalance, dataset inconsistency, model transparency, and inadequate utilization of deep learning models. The results of our review show that: 1) most deep learning models outperform classic machine learning and statistical algorithms in credit risk estimation, and 2) ensemble methods provide higher accuracy compared with single models. Finally, we present summary tables in terms of datasets and proposed models.

Internal ratings systems, implied credit risk and the consistency of banks’ risk classification policies

In This Issue

In portfolio credit risk models, correlated credit events are often modelled by means of correlated latent variables. The latent variables are interpreted as the firms’ asset values, and assumed to follow a normal distribution. A procedure is described that uses the information embodied in rating transition matrices to infer the shape of the latent variable distribution. Applying the approach to transition matrices of different origin yields consistent results. Compared to the normal distribution, the implied asset value distributions are fat-tailed, leading to a substantial increase of portfolio credit risk relative to the one under normality. The results are thus highly relevant for the design of credit risk measurement systems.

In literature there are different research results regarding the impact of borrower’s size on cyclicality of credit risk. The aim of this research is to determine whether the credit risk cyclicality increases with the size of the borrower, using data from Serbian banking sector. The research presented herein is one of the first for developing countries with this subject and where credit risk was approximated by the default rate. Empirical analysis of the time series of loan default rates, as dependent variable, and macroeconomic factors, as explanatory variable, is based on the panel error correction model. Panel units are risk segments. Amount of annual revenue is key criteria for granulation borrowers within key four risk segments (retail, micro, SME and large corporate) that corresponds to its size. In multi-factor model, research results confirm that there is long term relationship between macroeconomic factors and loan default rate in Serbian banking sector in all risk segments. However, in model where GDP is explanatory variable, in the segment of small- and medium-sized enterprises, the adjustment coefficient is not statistically significant. It can be inferred that the credit risk of the SMEs segment is the most resistant to changes in the business cycle phases.

Aiming to solve the difficulty in describing the high dimensional dependency structure of credit assets, we construct pair copula VaR model to evaluate the credit portfolio risk. The empirical study which takes the publicly traded companies in Shanghai stock exchanges and Shenzhen stock exchanges shows that the Clayton copula with Canonical vine structure is the most appropriate function to describe the high dimensional low tail dependency structure. Meanwhile, the Monte Carlo simulation result proves that the pair copula VaR model can accurately measure the credit portfolio risk both in calm period and crisis period. Additionally, we acquired the optimal weights of the different credit assets in portfolio according to the simulation results of pair copula VaR models. Based on the research results, the commercial banks can dynamically adjust their credit asset allocation, so as to alleviate the credit portfolio risk and conduct more efficient credit risk management.

In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer’s theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance sampling are used in rare event simulation for option pricing. We finally focus on large deviations methods in risk management for the estimation of large portfolio losses in credit risk and portfolio performance in market investment.

Under Basel II framework, credit risk assessment is of high significance in the light of correlation risk. Correlation risk is often envisioned along with business conditions and financial market’s impact. We employ copula methodology to identify the dependence structures that may exist between market risk fundamentals and credit risk fundamentals. Considering credit derivative spreads as credit risk fundamentals and market data as market risk determinants, we describe and quantify the asymmetric link prevailing between credit risk and market risk. Credit risk is negatively linked with market price risk whereas it becomes positively linked with market volatility risk. Such patterns give rise to interesting asymmetric dependence structures between both risk sources. We are then able to balance reliably market price risk with market volatility feedback, the market trend supporting a common correlation between securities. In the light of the previous trade-off, we propose also a simple credit risk management rule.