Model specification and collateralized debt obligation (mis)pricing

• Date: 01 November 2018
• Author: Sarah Qian Wang,Dan Luo,Dragon Yongjun Tang
• Published date: 01 November 2018
• DOI: http://doi.org/10.1002/fut.21932

Received: 20 September 2017

|

Revised: 20 April 2018

|

Accepted: 1 May 2018

DOI: 10.1002/fut.21932

RESEARCH ARTICLE

Model specification and collateralized debt obligation

(mis)pricing

Dan Luo

1,2

|

Dragon Yongjun Tang

3

|

Sarah Qian Wang

4

1

School of Finance, Shanghai University of

Finance and Economics, Shanghai, China

2

Shanghai Key Laboratory of Financial

Information Technology, Shanghai, China

3

Faculty of Business and Economics,

University of Hong Kong, Hong Kong,

Hong Kong

4

Warwick Business School, University of

Warwick, Coventry, UK

Correspondence

Sarah Qian Wang, Warwick Business

School, University of Warwick, Gibbet

Hill Road, Coventry CV4 7AL, UK.

Email: qian.wang@wbs.ac.uk

Funding information

Natural Science Foundation of China

(NSFC), Grant/Award Number:

71302075/G0206; Hong Kong Research

Grants Council, General Research Fund

HKU, Grant/Award Number: 17510016

Complex structured products, especially collateralized debt obligations (CDOs),

were at the center of the 2008 credit crisis. This paper explores the impact of

modeling difficulties on CDO mispricing. Comparing pricing outputs among

models with different specifications, we show that the use of a model with

advanced default correlation assumptions could have reduced the amount of

model‐implied AAA‐rated CDO securities. This pricing difference also has

predictive power for the subsequent downgrading of AAA‐rated CDO tranches.

However, the model specification is only qualitatively important for CDO

mispricing, as it has a modest quantitative effect in explaining the overall

pricing errors.

KEYWORDS

CDO, default correlation, frailty, model specification

JEL CLASSIFICATION

G12, G13, E43, E44

1

|

INTRODUCTION

The 2007–2009 credit crisis has had unprecedented impact on the financial industry.

1

At the center of this crisis is the

previously little known financial innovation called collateralized debt obligations (CDOs). CDOs are debt claims with

various seniorities against collateral asset pools. Senior claimholders will not suffer a loss until the subordinated

tranches are exhausted. Because of this prioritized structure and other credit enhancements, such as insurance, CDO

senior tranches had AAA credit ratings prior to the crisis. CDO issuance started in 1987 but remained dormant until

1997, with an annual issuance of $17 billion, since then the market has grown rapidly to reach an annual issuance of

$520.6 billion in 2006, according to Securities Industry and Financial Markets Association. CDO issuance peaked in

2007Q2 (quarterly issuance of $178.6 billion) and afterward declined exponentially (2009Q1 issuance $0.8 billion).

However, the strikingly strong recovery of the CDO market, especially collateralized loan obligations (CLOs), in recent

years has prompted significant concerns over the market and its valuation

2

Given the dramatic write‐downs associated

with CDOs during the credit crisis

3

and the resurgence of the CDO market in recent years, it is important to develop a

J Futures Markets. 2018;38:1284–1312.wileyonlinelibrary.com/journal/fut1284

|

© 2018 Wiley Periodicals, Inc.

1

Among the top‐five precrisis Wall Street investment banks, Lehman Brothers declared bankruptcy on September 15, 2008, Bear Stearns was acquired by J. P. Morgan on March 16, 2008, Merrill Lynch

was acquired by Bank of America on September 14, 2008, and Goldman Sachs and Morgan Stanley converted into bank holding companies on September 21, 2008.

2

See, for example “CLO surge prompts regulatory concerns,”Financial Times, September 8, 2014. CLO performance will remain solid in 2016 according to Moody’s Investors Service (2015). We are

also seeing a turnaround for the European CLO market. “Time looks ripe for European collateralised loan obligations,”Financial Times, January 21, 2016.

3

For instance, on July 28, 2008, Merrill Lynch sold $30.6 billion in notional value US super senior asset‐backed securities (ABS) CDOs to an affiliate of Dallas, Texas‐based private equity firm Lone Star

Funds for $6.7 billion, or 22 cents on a dollar. (Merrill Lynch also financed 75% of the sale through a loan with recourse only on those CDOs.)

good understanding of CDO valuation. We present a comprehensive study of CDO pricing with a focus on the impact of

model specification. Our study elucidates potential structural causes of CDO mispricing.

The innovative nature of CDOs makes it difficult to identify the exact reasons for this valuation failure before the

credit crisis. On the one hand, given the short history of the product and modeling difficulties, Duffie (2007) doubts that

anyone has capability to evaluate CDOs with comfortable accuracy. Accepting the complexities and modeling

difficulties, some journalists blame the quants and their models for “killing the Wall Street.”

4

On the other hand,

regulators and media have rushed to blame CDO underwriters and credit rating agencies, who brought CDOs to the

marketplace, owing to their potential conflicting incentives. While some market participants likely deserve more blame

than others, “careful research is needed to distinguish the relative importance of the bad incentives view and the

mispricing view,”as these two views have distinctly different implications for future regulation and risk management

(Allen, 2008).

Given the limitations in modeling techniques and historical data, large losses do not automatically imply risk

management failures (Stulz, 2008). This argument is particularly relevant for the current setting of CDOs, which are

collateralized on a pool of default‐risky assets. Accurate valuation of CDOs requires the joint distribution of those

assets, especially the default correlation, to be modeled. Defaults are rare events. Hence, the default correlation is

difficult to measure. Furthermore, even single‐obligor credit risk analysis is difficult. There is also little consensus on

the best practices for portfolio credit risk modeling. In this paper, we examine the impact of model specification on

portfolio credit risk evaluation and CDO mispricing.

5

Traditional portfolio credit risk models, such as that of Vasicek (1987), assume that the default correlation is driven

only by observable common factors. However, recent studies show that such an approach significantly underestimates

the actual default correlation (Das, Duffie, Kapadia, & Saita, 2007). Based on this observation, Duffie, Eckner, Horel,

and Saita (DEHS, 2009) propose a frailty correlated default model, in which the latent‐“frailty”factor is unobservable

and time varying. DEHS (2009) show that their model performs well in matching historical default patterns, and Collin‐

Dufresne (2009) also discusses the properties for good correlation models. Azizpour, Giesecke, and Schwenkler (2018)

find important roles of both frailty and contagion for default clustering.

Our simulation results on model specification substantiate the importance of the frailty factor to portfolio credit risk

valuation and CDO pricing. We focus on the tail risk that is most relevant to CDO senior tranches that are often rated

AAA. At the AAA level, the expected portfolio default loss rate is 5.4% higher when frailty is considered than when it is

not. Hence, ignoring the frailty factor would result in a 5.4% greater AAA tranche size. We further consider the impact

of correlation between macroeconomic factors on CDO pricing in the presence of frailty factor. In reality, there might

be correlation between macroeconomic factors. For example, when the market undergoes a crisis, the central bank will

step in and cut interest rates to inject liquidity into the market, which essentially creates a correlation between the

short‐term interest rate and stock market performance. However, our simulation results show that such consideration

of correlation between macroeconomic factors has little effect on portfolio credit risk valuation and CDO pricing when

the frailty factor is present.

Having examined the potential impacts of model specification on CDO valuation, we apply the DEHS frailty model

to historical CDO data. Our sample contains 237 CDOs issued between May 1998 and December 2004, including 46

collateralized bond obligations (CBOs), 82 CLOs, 99 CDOs collateralized with ABS (CDOs), which includes most

mortgage‐back securities, and 10 CDOs collateralized with other CDO tranche securities (CDO

2

s). When the credit

rating or pricing for CDOs is obtained, the collateral pool is typically incomplete. Rating agencies will thus conduct an

analysis and assign a rating based on the projected collateral pool characteristics. To price CDOs, we first generate

factor time series based on the CDO’s collateral pool characteristics. Then, we insert these factor time series into the no‐

frailty model (bad model) and the dynamic‐frailty model (good model) and generate the collateral pool loss distribution.

With the collateral pool loss distribution, we can determine the AAA tranche size by referring to the historical AAA

default probability.

6

We then compare the resulting AAA tranche size from the different model specifications (no‐frailty

vs. frailty model).

Our empirical findings are consistent with the simulation results. Specifically, the no‐frailty model generates lower

portfolio default rates and hence higher AAA tranche sizes than the results from a credit rating agency. The no‐frailty

LUO ET AL.

|

1285

4

See, for example, “Recipe for disaster: The formula that killed Wall Street,”Wired, February 23, 2009. Triana (2009) expressed similar views.

5

The issues on conflicts of interest and CDO security design are discussed by Griffin and Tang (2012) and Nicolo and Pelizzon (2008).

6

Section 2 discusses the tranche determination approach in details.