Excerpt

## Contents

List of Figures

List of Tables

List of Abbreviations

List of Symbols

1 Introduction

2 Theoretical Principles

2.1 Literature Review

2.1.1 Determinants of CDS Spreads

2.1.2 The CreditGradesTM Framework

2.2 Model Description

2.2.1 The Classical CreditGradesTM Model

2.2.2 Extensions to the CreditGradesTM Model

3 Descriptive Analysis

3.1 Data

3.2 Calibration

3.3 Descriptive Statistics

4 Empirical Analysis

4.1 The Extended CreditGradesTM Model

4.2 Case Study Analysis

4.3 Cointegration across Equity and CDS Markets .

4.3.1 Credit Spreads Long-Run Pricing Equilibrium

4.3.2 Price Discovery across Equity and CDS Markets .

4.3.3 Cointegration in the Peripheral Eurozone

4.4 Analysis of the Credit Spread Deviations

5 Conclusion and Outlook

A Appendix - Definitions

B Appendix - Summary Statistics

Bibliography

## List of Figures

2.1 CreditGradesTM Model Description

3.1 Historical 1000-days vs. Six-Months Implied Volatility

4.1 Model Implied vs. Market Observed CDS Spreads

4.2 Market vs Model Spreads - A Regional Comparison

4.3 The Lehman Brothers Case

4.4 The Bank of America Case

4.5 A graphical Analysis - The Eurozone

B.1 A graphical Analysis of US Banks

## List of Tables

2.1 Survival Probability Function

3.1 Goodness-of-Fit Analysis - Volatility and Debt-per-Share

3.2 Average Global Recovery Rate (*L*) across all Rating Classes

3.3 Sample Composition

3.4 Overview across Rating Classes

3.5 Summary of Macro-Economic Factors

4.1 Correlation Analysis - Model and Market CDS spreads

4.2 Error Measures - Model and Market CDS Spreads

4.3 Accuracy Analysis - the Lehman Brothers Case

4.4 Accuracy Analysis - the Bank of America Case

4.5 Accuracy Analysis - Eurozone

4.6 Cointegration Analysis - Full Sample

4.7 Cointegration Analysis - Eurozone

4.8 Summary Statistics - Macro and Firm Variables

4.9 Correlation Table

4.10 Regression Results

B.1 Overview of the Banking Universe

B.2 Yearly Observations of the Banking Universe

B.3 Overview of the Optimized *L* for each Bank

## List of Abbreviations

Abbildung in dieser Leseprobe nicht enthalten

## List of Symbols

Abbildung in dieser Leseprobe nicht enthalten

## 1 Introduction

In the recent years global credit institutions were characterized by insta- bilities, consolidations and high levels of distress, with the industry strongly depending on governmental support to avoid a full economical collapse ini- tiated by the unexpected default of Lehman Brothers. As a consequence of the strong state interferences as well as the implicit and explicit govern- mental guarantees in the midyear of 2010 the Global Financial Crisis turned into a Sovereign Debt Crisis in the peripheral Eurozone, especially for the so-called PIIGS countries (Portugal, Ireland, Italy, Greece and Spain). Con- sequently, global banks show a high level of interdependencies with their sovereigns and have been the most discussed industry in global economical markets during the last years. In such periods it is particularly important to understand the drivers of the credit risks within the financial industry. Therefore, the main purpose of this study is to explore the determinants of the credit risk for the global banking universe and to investigate these determinants for robustness during high volatile and structurally changing market environments.

The credit spread is referred to as the Credit Default Swap spread, which became the standard measure for credit risk in academic research due to its numerous advantageous over bond spreads.^{1} Blanco et al. (2005) argue that Credit Default Swap spreads are the easiest method to trade credit risk and highlight the more advanced base of market participants in credit derivative markets, while buy and hold strategies in bond markets cause illiquidity in secondary markets. Additionally, the derivative markets are free of trading restrictions such as limited shorting opportunities and tax effects, as shown in Elton et al. (2001). Parallel to these findings, Cossin et al. (2001) point out that Credit Default Swap contracts are directly writ- ten on credit events and are therefore free of bias caused by options or other covenants of the bond issues. The direct measurement of credit spreads in the derivative markets is therefore independent of a benchmark for the risk free yield. Finally, and most important Blanco et al. (2005) found empirical evidence for a lead relationship of Credit Default Swap spreads compared to bond spreads on an entity-specific basis, allowing a quicker incorporation of changes in the risk perceptions.

The academic research on the determinants of Credit Default Swap spreads has significantly evolved as a consequence of the advantageous characteris- tics of credit risk assessment in Credit Default Swap markets. Consequently, knowledge of the determinants of credit spreads is equally important to fi- nancial analysts, traders, risk managers and economic policy makers as pointed out by Alexander and Kaeck (2008). A starting point for most aca- demics is the empirical evaluation of the structural variables derived from the structural model framework as introduced by Merton (1974). Naturally, the sequencing step is to apply a model based on the structural framework to directly account for these input parameters. According to academics and practitioners the CreditGradesTM model derived by Finger et al. (2002) is considered to be the standard approach in pricing Credit Default Swap spreads for both academic and practical purposes.^{2} Therefore this study implements a specific calibration of the CreditGradesTM model, which in- corporates the state of the art extensions and adjustments suggested by academics.

The CreditGradesTM model is applied to estimate Credit Default Swap spreads of the financial institutions and to investigate the models accuracy in tracking market Credit Default Swap prices over time. Consequently, the appropriateness of the equity market variables in the structural model framework are implicitly investigated, whether the considered set of inputs and the model calibration adequately account for the specific character- istics of the banking universe, particularly through the Global Financial Crisis and the Sovereign Debt Crisis periods. An analysis of different sub- samples reveals additional insights of the governmental interventions into the banking sector during the Global Financial Crisis and Sovereign Debt Crisis periods. In fact, the bailout guarantees and state support are found to significantly distort the model performance caused by differently weighted effects in credit and equity markets. Furthermore, the interdependencies between the financial institutions and their sovereigns are also present in the Sovereign Debt Crisis period but effects are found to be reversed for some banks. Therefore, the hypothesis is formulated that structural models are not able to account for sovereign effects while evaluating the credit risk of banks.

This study is closely related to the study of Schweikhard and Tsesmelidakis (2012) who apply a similar model calibration and methodology to identify the impacts of governmental intervening on banks during the Global Financial Crisis period in equity and credit markets.

The present study differs in several points from related studies and contributes to the current research with extensions related to both the methodological calibration of the CreditGradesTM model and economical consequences emerging from governmental policies.

The model calibration formulated in this study is the first empirical research found to calculate the survival probability with the corrected ex- act survival probability function as suggested by Kiesel and Veraart (2008). The choice of the applied probability function is crucial for the model perfor- mance, particularly for the specific characteristics of the capital structure of credit institutions. Therefore, the underlying calibrations should out- perform the current state of research in terms of model performance and accuracy for the financial sector.

Furthermore, the performance of the CreditGradesTM model is for the first time specifically tested for a global banking universe, consisting of credit institutions from 12 countries and three continents, while compa- rable studies limited the analysis solely on one country. Therefore, this study can distinguish between country specific and particularly currency specific characteristics across the global banking universe. Consequently, case studies for selected banks and countries are conducted, revealing sig- nificant heterogeneous characteristics for some banks, even in the same cur- rency union. Additionally, the present study is to date the longest data set found, analysing almost nine years of market movements in equity and credit markets. Especially the coverage of two crises periods highlights the unique nature of the underlying data set. Actually, the Sovereign Debt Cri- sis makes its first appearance in the applications of structural models within this study.

The remainder of this study is organised as follows: The first part of Chap- ter 2 reviews the current state of literature both on the determinants of credit spreads and on the empirical applications of the CreditGradesTM framework. The second part in Chapter 2 describes the methodology of the CreditGradesTM model and introduces necessary extensions to calibrate the model on the specific demands of the banking industry. The underlying data set, the applied data manipulation and filtration and the calibration proce- dure to identify the best model fit are presented in Chapter 3. In Chapter 4 the full empirical analysis of the CreditGradesTM model is presented using the Statistical Software Package R (R Core Team (2013)). After analysing the general performance of the CreditGradesTM model, case studies are conducted highlighting bank and period specific observations. A detailed illustrations of the model behaviour for selected banks is provided in several cointegration analysis between stock, credit and sovereign markets. Finally, several panel regressions are analysed to identify the drivers causing the de- viations between market and model spreads. Chapter 5 concludes this study and presents an outlook for further investigations based on the underlying framework.

## 2 Theoretical Principles

The overview of the theoretical principals in this chapter is separated in two main parts. In the first part a review of existing literature is given, and the second part introduces the CreditGradesTM framework as developed by Finger et al. (2002).

### 2.1 Literature Review

The literature review focuses on two important areas in the field of credit risk pricing and provides the fundamental basis of this analysis. First, a review of the empirical evidence of factors determining Credit Default Swap (CDS) spreads is given. The goal is to identify additional input factors which are not incorporated in structural models, specifically in the CreditGradesTM framework. Moreover, evidence regarding the pricing ability of the CreditGradesTM framework will be reviewed. Additionally applications, extensions and methodologies based on the CreditGradesTM model for theoretical and practical purposes are presented.

#### 2.1.1 Determinants of CDS Spreads

In structural models the risk-free interest rate, the firm’s capital struc- ture and the firm’s asset volatility are amongst the factors that determine credit spreads and are accordingly named structural variables.^{3} Based on the input parameters in structural models as originally defined in Merton (1974), Black and Cox (1976) and Longstaff and Schwartz (1995) numer- ous researchers attempt to identify relevant determinants of credit spreads. An early study and therefore a benchmark for subsequent studies is con- ducted by Collin-Dufresne et al. (2001) testing the theoretical determinants of credit risk, the structural variables on corporate bond spreads. The au- thors are able to explain 25% of the variation in changes in corporate bond spreads. Additionally, they identified a common omitted factor by applying a principal component analysis.

With the increasing popularity of CDS markets, empirical researchers’ focus shifted towards the more liquid and direct CDS spreads as a measure of credit risk. Consequently, Cossin et al. (2001) analysed in one of the first studies on this topic the influence of the theoretical factors predicted by structural and reduced form models on CDS spreads. The variables analysed include among others the credit rating, the interest rates and the structural variables as mentioned above. For the period between January 1998 and February 2002 the authors analysed 392 CDS trades and are able to explain up to 82% of the variation in CDS spreads with the credit rating and structural variables being the most important determinants in univariate perspectives.

A similar study is provided by Abid and Naifer (2006), where the authors analysed 207 CDS trades for a global universe in the time period of May 2000 to May 2001. The variables analysed are the credit rating, risk-free interest rate, slope of the yield curve and the equity volatility. This combination of variables explains 66% of the variation in CDS market spreads, with credit rating being the most significant indicator.

Using the approximate arbitrage relationship in CDS and bond credit markets for a reference entity, Blanco et al. (2005) examined the credit risk dynamics between CDS and bond markets, where the CDS price is defined as the difference of a bonds’ yield and the reference risk-free interest rate. Considering 33 US and European investment grade reference entities for the period from January 2001 to June 2002 the authors found some evidence for this theoretical relationship in a long term perspective. They also found some reasoning for the observed deviation from this parity, where non-parity is due to the finding that CDS prices tend to lead credit bond spreads in pricing changes of default risk more quickly. Furthermore, the authors analysed the determinants of weekly changes in CDS and credit spreads applying multiple cross-sectional regressions. The authors conclude that macro factors have a greater impact on credit spreads than on CDS prices. On the other hand firm specific information add more explanatory power to CDS prices. Taking both factors into account the explained variance in CDS prices outperforms credit spreads and up to 25% of the variation in CDS spread changes are explained.

Ericsson et al. (2009) analysed in simple regression models the rela- tionship between theoretical determinants of credit risk and CDS spreads. Based on the structural variables the authors found evidence that their benchmark models only using these variables are both statistically and eco- nomically significant and therefore consistent with the underlying theory. Analysing the CDS spreads of individual firms in differences and levels the realized explained variance ranges for the benchmark model from 23% for the model in differences up to 60% in levels for the premia. Including addi- tional variables the explanatory power increases to 35% in changes and to 72% in levels. The positive theoretical relationship of leverage and volatil- ity with the CDS spread is validated in all regressional results, where the impact on CDS spreads of leverage tends to be strongest for time series data collection. Unlike in the time-series set, in cross-sectional analysis the strength of impact is reversed and equity volatility is the stronger driver of the CDS premia. This observation is explained to be due to the advanta- geous properties of the equity volatility providing information both about asset risk and leverage.

Fabozzi et al. (2007) also investigated the theoretical determinants of CDS spreads based on structural variables but also extended these inputs by specifically analysing the impact of liquidity. The input parameters are significant in pricing credit risk and explain up to 30% of the variation of CDS spreads. Firms with greater liquidity have greater CDS spreads as opposed to bond spreads. The authors argue that CDS contracts contain different economic characteristics, as a swap is a contract in which the value of the protection is paid in instalments, while a bond demands the credit risk to be paid in advance. Due to these contractual differences, the liquidity penalty is reflected differently in its prices.

Das and Sarin (2009) analysed CDS spreads of 230 firms with quar- terly data from 2001 to 2005 by additionally implementing accounting-based variables such as firm size, profitability and financial liquidity. Accounting based variables are able to explain CDS spreads similarly good as structural variables. A combination of both sources of input leads to the best results explaining about 72% of CDS market variation, suggesting complementary information in pricing distress.

In line with the previously introduced literature Greatrex (2009) explored the ability of structural variables to explain the variation in monthly CDS spread changes for the period from January 2001 to March 2006.^{4} Consistent with subsequent research the author identified leverage and volatility as key determinants of CDS spreads as suggested by the theoretical foundation of the structural framework.

Zhang et al. (2008) contributed to this field of research by explaining CDS spreads with equity volatility and the jump risks of individual firms in addition to structural variables calibrating a structural model based on Merton (1974). They found that the volatility risk and the jump risk add about 15% of explanatory power to the credit rating and structural fac- tors. These effects are strongest for high-yield and financially distressed corporates.

Further research applying similar analysis on the determinants of CDS spreads can i.a. be found in Hull et al. (2004) focussing on the event of rating announcements, Norden and Weber (2009) analysing the empirical relationship in CDS, bond and equity markets and Longstaff et al. (2005), who examined the relative pricing ability of corporate bonds and credit defaults swaps.

The study of Stulz (2010) is concerned with the contribution of CDS markets to the credit crisis. He found evidence that neither CDS or other derivative markets can be blamed for causing the financial crisis, nor that it worsened the crisis. Furthermore, the author highlights the advantages of derivative markets which actually helped reducing the negative financial implications and consequently contributed to robust economic growth over the last 30 years.

Finally, Casu and Chiaramonte (2011) investigated the performance of CDS spreads in pricing the credit risk of banks. The study analyses the period from January 2005 to March 2010 and therefore includes the high volatility period of the financial crisis. In a regression based framework the results indicate that bank CDS spreads reflect the risk captured by bank balance sheet fundamental variables. This result is consistent with the approach applied in this thesis, where a structural model is calibrated to model CDS market spreads of international banks for different periods.

#### 2.1.2 The CreditGradesTM Framework

The research on the CreditGradesTM framework recently increased sig- nificantly which shows the high interest for both CDS markets and struc- tural models. The literature review given in this section can be divided into two categories. The first category is concerned with possible extensions to the classical CreditGradesTM framework and the second category applies either the classical or extended versions to price CDS spreads. Only the most recent literature actually implements the CreditGradesTM model on pricing CDS spreads of financial firms. The focus in this section will there- fore lie on the research which both covers a long time period including the financial crisis and applies the CreditGradesTM framework to financial firms and banks specifically.

Extensions related to the classical CreditGradesTM framework were first introduced by Stamicar and Finger (2006) and Finger and Stamicar (2005). Both studies are concerned with the usage of historical equity volatility to approximate the asset volatility. Further concern is connected with the definition of the true level of leverage and whether the implementation of option skew information can improve assessing leverage on firm level over the fundamental approach suggested in the classical CreditGradesTM frame- work. Therefore, the authors introduced a linkage to equity option markets by estimating the asset volatility and the implied leverage by a combination of At-the-Money (ATM) equity options, Out-of-the-Money (OTM) equity options and CDS market spreads. Particularly, the advantage of option im- plied volatilities as a timely more accurate credit warning signal in credit crisis periods is highlighted by the authors. The advantage of inferring the leverage by implied volatilities are argued to overcome shortcomings in fi- nancial data reports and issues in determining the true level of leverage for firms with complicated capital structures such as banks. A more detailed elaboration on the extensions introduced by Stamicar and Finger (2006) and Finger and Stamicar (2005) is given in chapter 2.2.2. Related to the work of Stamicar and Finger (2006) and Finger and Stamicar (2005), Cao et al. (2011) and Cao et al. (2010) implement the CreditGradesTM model using both historical and option-implied equity volatilities to analyse the informa- tion content added by option-implied information. The analysis conducted in Cao et al. (2010) covers 301 firms (financial firms are excluded) for a period from January 2001 to December 2006 with daily observations. The regression-based framework clearly indicates that implied volatility mea- sures outperform historical volatilities in explaining CDS spreads and led the authors to the conclusion that the option implied volatility reflects both future expected stock volatilities and the volatility risk premium. Cao et al. (2011) contributed to this study by analysing the period from January 2007 to October 2009 and therefore ensuring the coverage of the financial crisis period. Additionally, Cao et al. (2011) show that the advantage of using option implied volatility gains importance for high volatile CDS spreads and for firms with lower credit ratings.

This research corroborates to the findings mentioned above and again highlight the advantages of building a linkage to equity option markets. Furthermore, Cao et al. (2011) and Cao et al. (2010) found proof for significant explanatory power of both firm-specific and macro variables, such as leverage, stock returns, liquidity and the risk-free interest rate.

In Kiesel and Veraart (2008) the survival probability function in the CreditGradesTM framework is specifically examined. The authors high- light two important improvements to the CreditGradesTM model by showing that the approximated survival probability function in the CreditGradesTM framework is only valid under certain circumstances and that the exact formula given in Finger et al. (2002) contains a mistake which Kiesel and Veraart (2008) correct and prove to be the favourable survival probability function in applying the model. Section 2.2.2 discusses the work of Kiesel and Veraart (2008) and the extensions mentioned therein in greater detail.^{5}

Mina and Ta (2002) were the first to apply the CreditGradesTM model for practical purposes. The authors estimate the issuer-specific risk for corporate bonds, where the expected losses are calculated using survival probability function of the CreditGradesTM framework. The issuer-specific risk is within their framework a component deriving the total risk of an issuer consisting of interest-rate and credit-spread risk. Additionally, an example is given on how to apply the CreditGradesTM probability of default function as a market-implied rating tool and how it adds information to agency ratings. Another approach in applying the CreditGradesTM model is conducted by Andrade et al. (2012) who use the CreditGradesTM framework to investigate the impact of the Sarbanes-Oxley Act.^{6} Therefore the authors interpret the Volatility of the Global Recovery Rate (*λ*) as the corporate opacity and calibrate *λ* by minimizing the sum of squared errors between market and theoretical CDS spreads. The analysis shows that the cost of debt and the corporate opacity decrease significantly after the Sarbanes- Oxley Act.

In Yeh (2010) an implementation of the classical CreditGradesTM frame- work is demonstrated for the financial crisis period from September 2007 to June 2009.

In a seminal study Yu (2006) implements the CreditGradesTM model to test for capital structure arbitrage strategies between equity and credit markets. In capital structure arbitrage strategies traders try to take advan- tage of relative and temporary mispricings across different security classes traded on the same capital structure.^{7} In that context, the study of Yu (2006) is the first large scale study which examines the profitability of such a strategy. The analysis covers daily observations of 261 North American industrial obligors over a period from 2001 to 2004. Large divergence be- tween markets leads the capital structure arbitrage strategy of Yu (2006) on a portfolio level to positive abnormal returns on the aggregate, but he also points out, that single trades can be very risky and can lead to se- vere losses. The highest losses in the study occurred for short position on the CDS spread, when spreads widened rapidly as a consequence of credit- event-like market situations. Under such circumstances equity hedges are ineffective and losses can be substantially for arbitrageurs.

In relation to the work of Yu (2006), Baljum and Larsen (2008) ap- ply a similar exercise, again only focussing on non-financial North Amer- ican firms over a period from July 2002 to September 2004. Besides the CreditGradesTM model, the authors use the extended Leland and Toft (1996) model to test the profitability of the capital structure arbitrage strat- egy. Different to Yu (2006), this study focussed on the major issues caused by possible model misspecification and mismeasured input variables. Con- sequently, a major finding is the importance of timely more accurate input factors to dominate the choice of which structural model to apply. The im- portance of the input parameter are also highlighted in Finger and Stamicar (2005), who found that implied volatilities outperform historical volatility measures. Consistently, Baljum and Larsen (2008) found in their specified sample that the arbitrage strategy is only profitable if option implied volatil- ity is used instead of historical volatility as opposed applied in Yu (2006). Excess returns using historical volatilities are shown to be insignificant. Consistent to the findings of Yu (2006) the authors confirm profitability of the strategy on a portfolio level and also highlight the high riskiness of single trades on the individual level.

An early study analysing the relationship between market CDS and stock implied CDS spreads using the CreditGradesTM framework is published by Byström (2006). The author examined in particular the correlation between the CreditGradesTM CDS spreads and two iTraxx CDS indices, which track the most liquid names in Europe. This study is found to be the first to include the financial sector applying the CreditGradesTM framework. The main results in this study, covering the time period from June 2004 to March 2006, show a strong correlation between theoretical and empirical iTraxx CDS index spreads. In regards to cross-serial and autocorrelation the study reveals that the iTraxx CDS index lags behind model spreads, which indicates the existence of prediction power of the CreditGradesTM model.

One of the first studies to analyse the performance of CreditGradesTM implied spreads is conducted by Stewart and Wagner (2008). The authors analysed the pricing performance of the CreditGradesTM model for 54 indi- vidual obligors from the Dow Jones CDX Investment Grade index universe. The time span from May 2004 to July 2006 is covered and the results are compared to the hybrid trinomial tree model of Das and Sundaram (2000). They found that on average the trinomial model by Das and Sundaram (2000) slightly outperforms the CreditGradesTM model and that both model performances can be poor for firms characterised by low correlation with a market proxy. However, the definition of the model parameters and the calibration processes conducted are not presented in detail, which make the results hard to compare to other research.

In Cserna and Imbierowicz (2008) the efficiency of the CDS market is analysed in terms of profitability and risk of capital structure arbitrage strategies. Three structural models, the CreditGradesTM model, a model introduced by Leland and Toft (1996) and finally the Zhou (2001) model are used to calculate the model CDS spreads and to identify mispricings in the CDS market. This is the first paper to adjust the default barrier and includes financial firms. The authors chose to set the default barrier at 8% of Total Liabilities, assuming a very simplified capital structure of banks. The dataset employed covers a global universe of 808 obligors in the period from January 2002 to December 2006. In terms of average pricing error, the model of Leland and Toft (1996) slightly outperforms the other models, where all models overestimate the market spreads. This result led the au- thors to conclude that complexity in the model definition generates larger arbitrage returns. Additionally, cross-sectoral and rating-partitioning anal- ysis reveals that the arbitrage returns are highest for high risk firms with a speculative rating grade. In the calibration of the model, the authors used historical equity volatility, which is shown to be suitable in quiet market environments by Finger et al. (2002), which actually was the case in the period of analysis between 2002 and 2006. Furthermore the work by Cserna and Imbierowicz (2008) highlights market inefficiencies for the CDS mar- ket until the years 2004 and 2005 which were overcome in the subsequent periods.

Strongly related and an extension to the research of Cserna and Im- bierowicz (2008) is given in Imbierowicz (2009). The first extension to the previous analysis is a wider time period, where the examined period be- gins in January 2002 and ends in April 2008, which consequently allows for the coverage of the financial crisis period. The second extension is based on panel regression analysis, which are conducted to identify missing macro economical factors that may explain the gap between CDS model and market spreads. Again a global universe consisting of European, Asian and North American obligors is formulated across all industry groups and through all rating-classes for a total of 759 obligors. Including the beginning of the financial crisis period, the author detected that the model of Zhou (2001) performs best for specific industries such as consumer goods, utilities and financials. In a cross-sectoral perspective though the CreditGradesTM model and Leland and Toft (1996) have about the same mean error in es- timating CDS spreads with a better fit in average compared to the Zhou (2001) model. Although the period analysed contains volatile market ob- servations, the author only used historical equity volatility measures in es- timating model spreads. This approach is inconsequential to the research mentioned above and to his own results in the panel regression analysis where the implied volatility is found to be a significant input parameter in explaining market CDS spreads. Furthermore, the results of the regression analysis suggest the consideration of forward-looking macro-indicators as well as liquidity measures in pricing CDS spreads which are not captured in structural models.

The study by Bedendo et al. (2011) is another example of investigating the relationship between equity and credit variables, implementing both the classical and the extended CreditGradesTM framework suggested by Stamicar and Finger (2006). The performances of the model spreads are compared on a cross-sectoral basis to market spreads for 54 North Ameri- can non-financial investment-grade obligors covering a time period between January 2002 and December 2005.^{8} The authors identify a significant corre- lation between both spreads in quiet periods but observe deviations between the theoretical fair value spreads from the models with CDS market spreads, where the gap is time varying and widens substantially in times of finan- cial turbulence. The increasing gap is explained due to more significant widening of model spreads compared to market spreads as a consequence of increasing volatility. In explaining the gap by applying panel regressions, the authors found CDS liquidity, changes of the volatility skew and changes of the option-implied volatility to be significant explanatory variables.

In the study of Rodrigues and Agarwal (2011) three structural models are implemented to investigate the pricing ability of credit spreads. Addi- tionally to the CreditGradesTM model, the classical Merton (1974) approach and Collin-Dufresne and Goldstein (2001) stationary leverage ratio model are tested. Despite that all model spreads are both highly correlated with market spreads and with each other, each model adds incremental informa- tion. On average, all model spreads individually understate market spreads across both sectors and rating classes. In terms of mean and median per- centage errors the CreditGradesTM model performs best, whereas testing the fit on an absolute level with mean and median absolute percentage er- ror the Collin-Dufresne and Goldstein (2001) model is observed to have the best fit. In a Fama and MacBeth (1973) regression framework and by regressing the individual model spreads on CDS market spreads, the CreditGradesTM slightly performs better in *R* ^{2} perspectives. Together with liquidity and credit rating variables the CreditGradesTM model spreads cap- ture up to 78% of the variation in market CDS spreads and actual spreads are overestimated including liquidity and credit rating as explanatory vari- ables. Rodrigues and Agarwal (2011) also include financial firms in their investigation, therefore it is insightful to see how the authors defined the leverage ratio in conducting the CreditGradesTM model. In all three models leverage is defined as the ratio of the book value of total debt to the sum of the market value of equity and the book value of total debt. As the CreditGradesTM framework is calibrated on a per-share basis, consequently adjustments to the approximation of the asset value are needed since the defined per-share basis in the CreditGradesTM framework is repealed.^{9}

Svec and Reeves (2010) conducted an analysis of capital structure ar- bitrage strategies on the Australian CDS market. The data analysed com- prises 25 investment grade firms listed on the Australian Securities Ex- change (ASX) covering the period between November 2005 and Decem- ber 2009. In consistence with Finger et al. (2002) but in contrast to e.g. Stamicar and Finger (2006), Cao et al. (2010) the 1000-day historical volatil- ity produces spreads with closer fits to market spreads compared to option- implied volatility. Opposed to this finding, the estimation of model spreads with option-implied volatility for the purpose of applying the capital struc- ture arbitrage strategy the returns significantly outperform the estimation and application using historical equity volatilities. Clear indication of a lead or lag relationship of actual spreads over model spreads applying Granger causality tests could not be observed for the underlying data set. The re- search conducted by Svec and Reeves (2010) additionally tested the model performance including financial firms and concluded that the consideration of financial firms did not significantly change any results found excluding financial firms. Other than in Cserna and Imbierowicz (2008) and Imbierow- icz (2009) the authors did not set a fixed default boundary as a proportion of debt, but left the Global Recovery Rate (*L*) a free parameter to cali- brate the capital structure while minimizing the gap between market and model spreads. This method was first introduced by Yu (2006), where the parsimonious input of total liabilities is conducted for calibration purposes.

The most recent study applying the CreditGradesTM framework is un- dertaken by Schweikhard and Tsesmelidakis (2012). Analysing the impact of governmental interventions on CDS and equity markets for a total of 497 U.S. obligors across all sectors and rating classes the authors provide evidence of a structural break in the valuation of U.S. bank debt, so that the credit and the equity markets decoupled during the financial crisis. They show that a possible explanation for this finding is the Too-Big-Too- Fail (TBTF) hypothesis, as some firms’ debt holders benefited from gov- ernment interventions during the bailout programs, where a shift of wealth from taxpayers to debt holders took place. The TBTF is measured as the gap between market and model spreads, which consequently increased in the financial turmoil, indicating that the stock-implied default risk has been much higher than CDS observations. The likelihood of a bank be- ing systematically relevant and therefore classified as TBTF increases with wider gaps, which from a policy perspective would imply successful inter- ventions in preventing further market escalation. During the financial crisis some other non-structural factors might have influenced CDS prices such as counter-party or liquidity risk, which are found to be significant in regres- sion analysis. Furthermore, cointegration analysis across CDS and stock markets indicate close movements in the long-term and similar contribution to price discovery. As the main focus of this study is the investigation of banks in the financial crisis period, this is the closest research found to the research conducted in this thesis. In terms of the model calibration, the cap- ital structure of banks is analogously approximated as in Svec and Reeves (2010), where *L* is left a free parameter to adapt for the total liabilities as the real leverage of banks is difficult to assess.

### 2.2 Model Description

This section starts with an introduction of the theory and model def- inition of the classical CreditGradesTM framework as developed by Finger et al. (2002). The initial set-up of the framework is implemented to apply the model to industrial firms only and was calibrated in a quiet market envi- ronment in the period of 2001 to 2002. Therefore some major shortcomings of the model are observable in applying the classical CreditGradesTM frame- work. Consequently, extensions are necessary to overcome these shortcom- ings, which are introduced in the second part of this section. These exten- sions are introduced by Kiesel and Veraart (2008), who are concerned about the survival probability functions given in the CreditGradesTM framework and Stamicar and Finger (2006), who add a link to equity option markets to improve the CreditGradesTM model in pricing CDS spread levels, partic- ularly in volatile market environments.

#### 2.2.1 The Classical CreditGradesTM Model

Structural models are based on the framework first introduced by Black and Scholes (1973) and Merton (1974) linking credit and equity markets. In Merton (1974) a firm is assumed to have a certain amount of zero-coupon debt which will be due at maturity *T*. A firm’s default occurs when the asset value falls below the promised debt repayment of the underlying instrument at time *T*.^{10} A classical criticism of of the Merton (1974) model is due to the limitation that default can only occur at the end of the maturity *T*, causing an underestimation of short-term credit spreads.

In Black and Cox (1976) a first extension of the Merton (1974) frame- work is introduced allowing for bankruptcy to occur during the lifetime of the security. This type of model is often referred to as first time passage models.^{11}

In line with the Black and Cox (1976) framework the CreditGradesTM model was jointly developed by a grouping of Deutsche Bank, Goldman Sachs, J.P. Morgan and Risk Metrics in May 2002.^{12} The model is a sim- plified version of the Merton (1974) and Black and Cox (1976) framework where the default probability is derived as a function of the stock volatil- ity and the leverage ratio.^{13} According to the authors the CreditGradesTM model is “a practical implementation of the standard structural model” which “purpose [. . . ] is to establish a robust but simple framework linking the credit and equity markets.“^{14}

In fact the model is simple to implement and transparent in applications using only a small number of openly accessible and observable inputs leading to a very attractive model for both academics and practitioners.

While Merton (1974) assumes default to occur when the firms asset value drops below its fixed debt value at maturity *T*, the CreditGradesTM model introduces uncertainty into the default barrier. The randomness simulates the fact that the real level of a firm’s liabilities is usually unknown until the event of default occurs. This is caused by infrequent balanced sheet information which are only reported quarterly and might be distorted or manipulated due to accounting practice.^{15} Figure 2.1 summarises the main assumptions of the CreditGradesTM model.

The firms *V* 0 is approximated as:

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.1: CreditGradesTM Model Description^{16}

This figure presents the main assumptions of the CreditGradesTM framework. These main assumptions are the Brownian motion process of the Asset Value (*V* 0 ) and the uncertainty introduced to the Default Barrier (*L D*)

Abbildung in dieser Leseprobe nicht enthalten

where * S* is the firm’s stock price, *L * is the Average Global Recovery Rate and *D* is today’s Debt-per-Share (DPS). All relevant firm variables are expressed on a per-share basis. The asset value *V* 0 is assumed to follow a geometric Brownian motion process similar to the Merton framework:

Abbildung in dieser Leseprobe nicht enthalten

with *Wt* being the standard Brownian motion, *σ* is the firms asset volatility and *μ D* is the asset drift. The asset drift *μ D* is assumed to be zero as firms are expected to manage debt and stock dividends to maintain the leverage level steady over time and is therefore consistent with Collin-Dufresne and Gold- stein (2001) where leverage is assumed to be stationary and consequently mean-reverting.^{17} The solution to the stochastic differential equation in (2.2) is:^{18}

Abbildung in dieser Leseprobe nicht enthalten

The asset volatility is approximated from the theoretical relationship be- tween asset and equity volatility, *σ* respectively *σ E* and shown in (2.4):

Abbildung in dieser Leseprobe nicht enthalten

As mentioned above rather than using a fixed default barrier as in the Merton (1974) model, randomness is introduced to the default barrier *LD * in the CreditGradesTM model and is consequently supposed to follow a stochastic process.^{19} By multiplying the average Average Global Recovery Rate (*L*) with the company’s DPS *D*, the default barrier is adjusted to estimate the firm’s asset value which actually is available to debt holders in the occurrence of bankruptcy. The recovery rate *L* is assumed to follow a log-normal distribution with mean *L* and the percentage standard deviation *λ*:

Abbildung in dieser Leseprobe nicht enthalten

where *Z* is a standard normal random variable and independent of the Brownian motion *W*. Thus, the uncertainty of the actual level of a firm’s DPS is captured by letting *Z* be random. The true level of *L* does not evolve over time under this condition and is not possible to be observed with certainty. Consequently, with the uncertain recovery rate the default barrier *LD* can be hit unexpectedly, leading to a jump-like default event. Accordingly, the default event occurs when the firm’s asset value crosses the default barrier for the first time. This is one of the major improvements over Merton’s model, where the default barrier is fixed which does not allow for jump-like default-events, resulting in unrealistic low short-term spreads. This means that firms who start with asset values above the default barrier cannot reach the barrier immediately by diffusion only.^{20} The default condition is thus derived from equations (2.3) and (2.5) and is formally defined as:

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The survival probability *P* of the company at time *t* is defined as the firm’s ability to ensure its total debt service and therefore the probability that the asset value does not reach the barrier before time *t*, as seen from today (*t* = 0) and as presented in (2.6). The process *X* in (2.7) is introduced to determine the survival probability:

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then (2.6) can be rewritten to:

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For *t ≥* 0, *X _{t}* follows a normal distribution with:

Abbildung in dieser Leseprobe nicht enthalten

and

Abbildung in dieser Leseprobe nicht enthalten

Two alternatives to determine a formula for the survival probability function are shown in the CreditGradesTM framework. The first and pre- ferred method by Finger et al. (2002) is to approximate *X* as such that the approximation does not contain the random variable *Z* any more. This approximation is based on the assimilation of *X* to a Brownian motion with matching moments. The approximation therefore replaces the uncertainty in the default barrier with an uncertainty in the level of the firm’s value at *t* = 0. The survival probability *P* (*t*) is then derived as a closed-form for- mula, estimation the probability of survival up to time *t*. The final function of the approximated survival probability was first derived in Lardy et al. (2000) and is given in (2.11)^{2122}:

Abbildung in dieser Leseprobe nicht enthalten

where

Abbildung in dieser Leseprobe nicht enthalten

and Φ(*a*) is the cumulative normal distribution function given as:

Abbildung in dieser Leseprobe nicht enthalten

The second method to determine the survival probability *P* (*t*) is the derivation of the exact formula by integrating the random variable *Z* out and still getting a closed-form solution that contains the cumulative bivariate normal distribution Φ2(*a, b, ρ*)^{23}:

Abbildung in dieser Leseprobe nicht enthalten

where the cumulative bivariate normal distribution Φ2 is given as:

Abbildung in dieser Leseprobe nicht enthalten

This exact formula (2.16) as given in Finger et al. (2002) contains an error which is shown by Kiesel and Veraart (2008) and is further highlighted in the next paragraph where the correction of Kiesel and Veraart (2008) is introduced as an important extension of the CreditGradesTM framework to calculate adequate credit spreads for financial institutions.

For the purpose of calculating a credit price the CreditGradesTM survival probability function needs to be converted. Therefore two additional input parameters are specified: the risk-free interest rate *r* and the recovery rate *R * on the underlying credit. While *L* is the expected Average Global Recovery Rate over all credit classes, * R* differs from *L* in the way that * R* represents the expected recovery on a specific class of a firm’s debt, in this case the class of senior unsecured debt.

Given all specified input parameters the CDS can be priced by solving for the continuously compounded spread *c** such that an equilibrium between the premium paid by the protections’ buyer and the expected loss payouts of the seller is ensured.

**[...]**

^{1} The credit spreads and Credit Default Swap spreads express consequently the same measure and are treated equally within this study.

^{2} See for example Yu (2006), Bedendo et al. (2011) and Löffler and Posch (2011).

^{3} Collin-Dufresne et al. (2001), pp. 2180-2181, Cossin et al. (2001), p. 24 and Greatrex (2009), p. 20.

^{4} The authors apply the analysis to CDS spread changes, since they are concerned with CDS spreads being nonstationary and consequently causing spurious results in applying regression analysis on CDS spread levels.

^{5} Another series of researchers extended the CreditGradesTM framework in introducing jump-diffusions to the asset value process. Beginning with Sepp (2006), Ozeki et al. (2011) and He et al. (2011) these models are capable of capturing the skewness of market implied volatilities. Please refer to these studies for further information and more detailed elaborations.

^{6} The main objective of the Sarbanes-Oxley Act is to recovery for the public trust in US capital markets, which suffered from accounting scandals by increasing corporate transparency through more reliable corporate reporting.

^{7} See Baljum and Larsen (2008),p. 1.

^{8} The CDX.NA.IG index provided by the Markit Group initially covered 80 obligors. As stated in Bedendo et al. (2011) (pp. 662-663) this number was reduced implementing the second extension suggested by Stamicar and Finger (2006) implying asset volatility and leverage from the volatility skew of equity options. The complex model definition leads to errata pricing theoretical CDS spreads, therefore all firms containing unrealistic spreads were eliminated from the data set.

^{9} As a consequence the asset value should be approximated by the market value of equity divided by sum of the market value of equity and the book value of total debt plus the book value of debt divided by the sum of the market value of equity and the book value of total debt. The authors do not contribute any information to the suggested adjustments.

^{10} See Hull et al. (2005), p. 5.

^{11} For example in Longstaff and Schwartz (1995), Zhou (2001) and Goldberg and Giesecke (2004).

^{12} See Cao et al. (2011), p. 67.

^{13} See Byström (2005),p. 4.

^{14} See Finger et al. (2002), p. 5.

^{15} See Löffler and Posch (2011), p. 44

^{16} See Finger et al. (2002), p. 7.

^{17} See Collin-Dufresne and Goldstein (2001), pp. 1949-1950.

^{18} See Neftci (2000).

^{19} See Finger et al. (2002), p. 6.

^{20} See Kiesel and Veraart (2008), p. 65.

^{21} For a more detailed elaboration of the derivation and the approximation of the survival probability function please refer to Lardy et al. (2000).

^{22} The convention that log denotes the natural logarithm is adopted within this thesis.

^{23} See Kiesel and Veraart (2008), p. 66.

- Quote paper
- Anonymous, 2013, Determinants of Credit Spreads of Financial Institutions, Munich, GRIN Verlag, https://www.grin.com/document/308331

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