Structural Vs Reduced Form Models

Published Date: 02 Nov 2017

Generally, it is not worthwhile to have a major gap between the regulatory and the "true" economic capital. A homogenization of these values is one goal of the new Capital Accord and would simplify the management of the credit portfolio.

Hamerle, Liebig and Rosch (2003) are trying to find some similarities between models proposed by Basel II and those which are used by practitioners. They were able to find some similarities with CreditMetrics in the way how probabilities of default (PDs) are calculated.

Structural vs. Reduced-form models

In literature we can find two fundamental approaches which are used in credit risk valuation process: reduced-form models and structural models. Besides those models are designed to be used to measure credit risk, almost all of those models are also used in pricing risky bonds, such as bonds issued by corporates, and pricing credit derivatives, such as credit swaps, credit spread options, and collateralized debt obligations (Schmid, 2004). In addition, each model group has various types. Even though, there are big amount of credit risk valuation models, it is challenging to define and incorporate default correlations into a model. Incorporating default correlations in any portfolio credit risk analysis is difficult because of the lack of good data on default correlations, and the complexity of developing realistic models of default correlations that capture its dependence on credit quality, region, industry and time horizon (Nagpal and Bahar, 2001). Zhou (1997) is also naming valuation of default correlation as an important task in credit analysis and risk management. Saunders and Allen (2002) gives more detailed theoretical background about default correlations in one of the most popular credit risk management framework (KMV’s Portfolio Manager). Later in his works (Saunders and Cornett, 2008) Saunders uses his remarks to apply default correlation to the credit risk models. This approach is not really convincing because different portfolios should have different default correlation, and for different portfolios you should calculate default correlation separately.

Then talking more about reduced-form models and structural models we can find in literature that it can be characterized in terms of information known by the modeler (Jarrow and Protter, 2004). Jarrow et. al. (2004) says that structural models assume that the modeler (who is modeling credit risk of specific firm – authors remark) has the same information set as the firm’s manager – complete knowledge of all firm’s assets and liabilities; reduced-form models assume that the modeler has the same information set as the market – incomplete knowledge of firm’s condition. In the paper Jarrow and Protter are analyzing theoretical assumptions made by other authors and are trying to prove their hypothesis that reduced form-models and structural models can be described by known information. However, theory is always not enough. Arora, Bohn and Zhu (2005) in their paper are empirically comparing two structural models (Merton model, the Vasicek-Kealhofer (VK) model) and one reduced-form model (Hull-White (HW)). They have tested the ability of the Merton model and VK model to discriminate defaulters from non-defaulters based on their default probabilities generated from information known in the equity market. Also they did test the ability of the HW model to discriminate defaulters from non-defaulters based on default probabilities generated from the information known in the bond market. They came up with the conclusion that despite the advantages stated by proponents of reduced-form models, a HW reduced-form model largely underperforms a sophisticated structural model like that of the VK. HW model can outperform more sophisticated structural models in terms of explaining the cross –sectional variation of CDS spreads (Arora et. al., 2005).

Statistical measures in Credit risk

In addition, credit risk assessment methodologies are also using of different statistics measurement such as: distance-to-default, Expected Shortfall, Value-at-risk, probability of shortfall, and others. Distance-to-default (DD) was first introduced to commercial usage by Moody’s KMV, it has become a widely used statistical measure of credit risk for nonfinancial corporations. Jorge, Chan-Lau and Amadou (2006) in their working paper says that the application of the distance-to-default to measure risks in financial institutions is not straightforward partly due to the differences between the liabilities of these institutions compared to those of nonfinancial corporations. However, empirical studies have shown that the distance-to-default predicts well ratings downgrades of banks in developed countries and in emerging market countries (Jorge et. al., 2006). Value-at-risk (VaR) is probably the most commonly reported statistical measure of credit risk. Gourieroux and Jasiak (2009) define the VaR of a portfolio as the amount risked over some period of time with a fixed probability. VaR provides a more sensible measure of the risk of the portfolio than variance since it focuses on losses, although VaR is not without its own issues (Gourieroux and Jasiak, 2009). Expected shortfall (ES) according to same Gourieroux and Jasiak (2009) is also known as tail-VaR – combines aspects of the VaR methodology with more information about the distribution of returns in the tail. However, practitioners and academics are actively discussing about the effectiveness of these measures in characterizing risk. For example, Duffie and Singleton (2003) says that VaR alone should be considered an insufficient measure for understanding credit risk. Dependence on a single risk measure has a problem in disregarding important information on the risk of portfolios. Question "Why?" is also answered by Yamai and Yoshiba (2002), they were making the research about usage of VaR and Expected shortfall in financial risk management. They came up with the conclusion that the use of VaR and expected shortfall should not dominate in financial risk management. To capture the information disregarded by VaR and expected shortfall, it is essential to monitor diverse aspects of the profit/loss distribution, such as tail fatness and asymptotic dependence (Yamai and Yoshiba, 2002).

Surveys

Practitioners do apply a number of standard structures for credit risk modeling and management, however the detailed information about implementation of those models is not provided. To find out answer to the question what models are used in practice, we need to analyze several surveys. The survey results which are provided in the literature can be explored to determine the most commonly used credit risk management structures among banks and financial institutions.

One survey we could find in the literature is the made by Fatemi and Fooladi (2006). The purpose of the survey was to investigate current practices of the largest US-based financial institutions (Fatemi and Fooladi, 2006). 21 usable responses out of 100 surveyed banks were collected. While analyzing the results we can identify that biggest number of respondents used or are planning to use KMV’s Portfolio Manager and a little bit behind is CreditMetrics™. Some of banks are also using CreditRisk+ and McKinsey’s Credit Portfolio View got zero points from this survey.

Second survey I am describing was made by Rutter Associates in 2002. Responses were collected from 41 out of 71 sent surveys. When asked does you use credit portfolio model 85% of respondents answered positively, 69% of them use Portfolio Manager, 20% - CreditManager® (an application based upon the methodology of RiskMetrics CreditMetrics™). Other 6% of positively responded survey participants use MacroFactor Model and 17% of respondents use Internally-Developed model. In addition to these models, the CreditPortfolioView framework developed by McKinsey & Company is one more model which we can frequently find in the literature, but rarely shows in use of practitioners.

Besides previously described surveys there were also surveys made among Lithuanian banks. Vytautas Valvonis has made a survey in order to determine how credit risk management is organized in Lithuanian banks. The survey was sent to 9 banks, 6 of them responded to the survey. To the question what credit risk management models do banks use, 3 banks answered that they use expert based models and 3 - mixed models (unfortunately expert based models and mixed model were not defined).

Moreover, European Central Bank (2007) states that CreditMetrics™ methodology (…) is used or being tested by most central banks participating in the task force, either directly, using the CreditManager® software, or through in-house systems (developed in Matlab® or Excel®) using a similar methodology.

CreditMetrics, KMV Portfolio Manager and CreditRisk+ Overview

In this part of thesis I will briefly introduce three main portfolio credit risk management methodologies. This part covers only definitions of the models; the methodological part will be given in the further section.

CreditMetrics

CreditMetrics framework proposed by J.P. Morgan is one of the portfolio credit value-at-risk models. Gupton et al. (1997) give details of CreditMetrics as follows. CreditMetrics essentially utilizes the fact that if asset returns (percent changes in assets value) of a firm, namely an obligor, fall below a certain threshold, then that firm defaults. In fact, CreditMetrics is not a pure-default or default-mode model, meaning a model which accepts loss only in case of a default. It combines the default process with credit migrations which correspond to rating transitions. These kinds of models are called Mark-to-Market Models. So, by applying forward yield curves for each rating group, CreditMetrics is able to estimate credit portfolio value and the unexpected loss of a credit portfolio. In that manner, as Crouhy et al. (2000) state that CreditMetrics is an extended version of Merton’s option pricing approach to the valuation of a firm’s assets since Merton only considers default.

Although CreditMetrics offers the estimation of joint credit quality migration likelihoods as a way of observing the correlation structure, it is not very practical to do so when dealing with extremely large credit portfolios. Then the portfolio is extremely large, to estimate joint credit quality migration likelihoods will require a huge data set. For these reasons, it handles the correlations between obligors by introducing a multifactor model. In a multifactor model, a latent variable triggers a change (default or rating transition [1] ) in the credit worthiness of a firm. Furthermore, in CreditMetrics framework, the asset return of a firm is used as a latent variable driven both by systematic risk factors, such as country index, industry index and regional index, and by a firm specific factor (nonsystematic or idiosyncratic risk factor). However, CreditMetrics proposes the use of equity returns to reveal the correlation structure of a credit portfolio instead of asset returns while asset returns are not always observable in the market. Yet, equity correlations are not equal to asset correlations. This assumption does not take into account the firm leverage effect on asset values (Jacobs, 2004). By examining the effect of different systematic factors (for instance, country-industry index) over the changes in equity of a firm and time series data belonging to those systematic factors, one can determine the correlation structure.

KMV Portfolio Manager

KMV Portfolio Manager is another mark-to-market portfolio VaR model while it also considers credit quality changes due to rating migrations. Also, as explained in the previous section the framework does not use transition matrices and instead it models the default rates in a continuous manner. This approach can be seen as an enhancement of J. P. Morgan’s CreditMetrics. Crouhy et al. (2000) shows and explains the results of Moody’s KMV’s simulation test that reveals significant deviations of actual default and transition probabilities from average probabilities. Moreover, Portfolio Manager covers the calculation of each obligor’s actual default probability, which is named as Expected Default Frequency (EDF) by Moody’s KMV. Another substantial improvement of Portfolio Manager is that these EDFs are firm specific, so any rating or scoring system can be used to match these probabilities (Crouhy et al., 2000). On the other hand, this framework is still based on Merton’s (1974) firm valuation approach (Schmid, 2004). Simply, if the market value of a firm’s assets falls below the total debt value, then that firm is said to default. Therefore, the price of a put option written on the asset value of a firm with a strike price equal to that firm’s total debt gives us the risk.

Contrary to Creditmetrics, KMV Portfolio Manager uses asset values of firms as risk drivers since correlated asset values straightforwardly act as a trigger to correlated default events (Bessis, 2002). Kealhofer and Bohn (2001) explain the model used by Portfolio Manager as follows. Portfolio Manager first derives current asset value and asset volatility (percent change) of a firm (obligor) from time series data of that firm’s equity value and its fixed liabilities. As seen in figure 1, equity is nothing but the difference between the value of a firm’s assets and its liabilities; moreover, current equity value can be directly calculated by the following famous Black Scholes-Merton option pricing formula under the assumption that the percentage change in a firm’s underlying assets follows the stochastic process.