A hybrid information approach to predict corporate credit risk

• Author: Simone Kelly,Di Bu,Qing Zhou,Yin Liao
• Published date: 01 September 2018
• DOI: http://doi.org/10.1002/fut.21930
• Date: 01 September 2018

Received: 27 September 2016

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Revised: 15 April 2018

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Accepted: 17 April 2018

DOI: 10.1002/fut.21930

RESEARCH ARTICLE

A hybrid information approach to predict corporate

credit risk

Di Bu

1

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Simone Kelly

2

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Yin Liao

3

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Qing Zhou

1,4

1

Macquarie University, Sydney,

New South Wales, Australia

2

Department of Finance, Business School,

Bond University, Robina, Queensland,

Australia

3

School of Economics, Business School,

Queensland University of Technology,

Brisbane, Queensland, Australia

4

School of Management, Xi’an Jiaotong

University, Xi’an, China

Correspondence

Yin Liao, Department of Finance,

Business School, Bond University,

14 University Dr, Robina,

QLD 4226, Australia.

Email: yin.liao@qut.edu.au

Funding information

NSFC, Grant/Award Number: 71602158

This study proposes a hybrid information approach to predict corporate credit risk.

In contrast to the previous literature that debates which credit risk model is the best,

we pool information from a diverse set of structural and reduced‐form models to

produce a model combination based on credit risk prediction. Compared with each

single model, the pooled strategies yield consistently lower average risk prediction

errors over time. We also find that while the reduced‐form models contribute more

in the pooled strategies for speculative‐grade names and longer maturities, the

structural models have higher weights for shorter maturities and investment grade

names.

KEYWORDS

bond spread, corporate credit risk, model combination, reduced‐form model, structural model

JEL CLASSIFICATION

C22, G13

1

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INTRODUCTION

The valuation and prediction of corporate credit risk is an important topic in both empirical and theoretical research. The

structural and reduced‐form models are two competing paradigms in this study field, and the literature (Jarrow & Protter,

2004) differentiates between the two modeling frameworks from the information perspective. In structural models, the

modelers, as the firms’managers, are assumed to have complete knowledge of the firms’assets and liabilities. The corporate

default, therefore, occurs when the firm’s value hits a default barrier. In contrast, the reduced‐form models show that the

modelers have incomplete knowledge of the firm’s conditions as normal market participants, in which the firm’s default time is

not accessible and can be simply specified by a hazard rate process. While early studies debate which modeling framework

between the two better captures credit risk and conclude that all the credit risk models consistently underpredict corporate

bond spreads (e.g., Eom, Helwege, & Huang, 2004; Collin‐Dufresne & Goldstein, 2001), in this paper, we combine the two

modeling frameworks together and propose a model combination approach to improve corporate credit risk prediction.

From the modeling framework, we choose two classic representatives to form the model pool. The first structural model we

consider is the Merton model (Merton, 1974), which serves as the cornerstone for all the other structural models. The Merton

model regards corporate liabilities as contingent claims on the assets of firms and applies option theory to derive the value of a

firm’s liabilities in the presence of default. In doing so, the firm’s equity value can be viewed as a call option on the value of the

firm’s assets, and default will occur if the firm’s assetvalue is not enough to cover the firm’s liabilities. Despite theMerton model

building up the theoretical foundation for the structural models, most assumptions in the model are not held in reality. Therefore,

we consider the second structural model, the Black–Cox model (Black & Cox,1976), in which the default occurs beforethe end of

the debt maturity. Additionally, instead of considering only a single type of debt, the model allows for a tranche structure in the

J Futures Markets. 2018;38:1062–1078.wileyonlinelibrary.com/journal/fut1062

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© 2018 Wiley Periodicals, Inc.

senior and subordinated bonds. The formulations of the two structural models are consistent with the manager’s the perspective

that the firm’s condition is observable and that default is an accessible stopping time.

The two classic reduced‐form models we considered here include the Jarrow and Turnbull (JT) model (Jarrow & Turnbull,

1995) and the Duffie and Singleton (DS) model (Duffie & Singleton, 1999). The two reduced‐form models treat the default as

an unpredicted event given by a hazard process; hence, the firm will default when the exogenous random variable changes its

level over a certain time interval. As a result, the default event is not dependent on the value of the firm’s asset. Specifically,

the JT model assumes that the recovery rate is exogenous and that recovery can only be received at the time of maturity if the

default occurs prior to maturity. The DS model extends the JT model byallowing the recovery payment to be made at any time.

Therefore, constructing reduced‐form models presumes that the market does not have the same information set as the firm’s

management. The imperfect knowledge of the market is because of the fact that accounting reports and/or management press

releases either purposefully or inadvertently add extraneous information that obscures the knowledge of the firm’s asset value

(Cetin, Jarrow, Protter, & Yildirim, 2004), leading to an inaccessible default time.

Given the distinct information foundation of these models, we propose combining the aforementioned four credit risk

model representatives to construct a hybrid information‐based forecast for corporate credit spread. The model combination has

been widely used in econometric forecasting since the pioneer work by Bates and Granger (1969). The model combination

method was later extended by Granger and Ramanathan (1984) and has spawned much literature. Some excellent reviews

include Clemen (1989), Diebold and Lopez (1996), Clements, Hendry, and College (2002), and Timmermann (2006).

Recently, forecast combinations have received renewed attention in the macroeconomic forecasting literature (e.g., Stock &

Watson, 2003) and increasing attention in finance (e.g., Rapach, Strauss, & Zhou, 2010; O’Doherty, Savin, & Tiwari, 2012;

Durham & Geweke, 2014). Because the underlying market condition changes over time, the firm asset returns and default

events are generated from different data‐generating processes over distinct economic states. Thus, there is no single model

dominating all others in all the market conditions or economic states. The combination of different models with dynamically

updated weights would allow for this model uncertainty. In addition, previous empirical studies (e.g., Gündüz & Homburg,

2014) suggest that the reduced‐form approach outperforms the structural models for investment‐grade (IG) names and longer

maturities, and the structural approach performs better for shorter maturities and sub‐IG names. Given the cross‐sectional

dispersion of the model performance in different types of corporate debts, the model combination would result in better

performance on average across a wide range of corporate debts. To accommodate the above arguments, we implement a bias–

variance trade‐off framework to achieve the combination. We first decompose the forecast errors of each individual model into

bias and variance components. Then, we determine the optimal weights for individual models by achieving global minimum

variance. Last, we correct the bias by assuming the prediction bias that this period is the same as that of the last period. The

pooled model, therefore, has the minimum variance and negligible bias.

Next, we gauge the empirical performance of our combined models in corporate bond spread prediction. Our data set

consists of 279,826 monthly corporate bond yield spreads to the swap rate of noncallable bonds issued by industrial firms over

the period 1992–2016. We first explore the ability of both the combined model and all the individual models to explain the

cross‐sectional variation of bond spreads across different maturity ranges and credit ratings. We find that the performance of

the combined model is constantly superior to other four individual models with 99% confidence level for all maturity–rating

buckets in terms of root mean square error (RMSE). When looking at the performance of the individual models, we find that

the reduced‐form approaches outperform the structural for speculative‐grade (SG) credit bonds and longer maturities, while

the structural models do better for IG credit and shorter‐term bond spreads. Structural models assume complete knowledge of a

very detailed information set, akin to that held by the firm’s managers, while reduced‐form models assume knowledge of a less

detailed information set, akin to that observed by the market (Jarrow & Protter, 2004). Taking this insight, we can interpret the

results from information perspective by saying that the lower the credit rating and longer the term of the bonds, the harder it is

for bond holders to access the complete knowledge of the bond’s condition. Therefore, the assumption of reduced‐form models

is more realistic than that of structural models, resulting in a better empirical performance for SG and longer‐term bonds.

Similar results for individual models are also reported by Gündüz and Homburg (2014). Second, using time‐series regression,

we test whether the combined model can also better capture the time variations in corporate bond spread than the individual

models and find that the combined model also significantly outperforms in both stable and volatile periods.

Our work makes three contributions to the corporate credit risk literature. First, it improves the performance

of credit risk models for corporate credit spread forecasts by combining the two well‐known competing model classes.

As a barometer of the financial health of corporations and sovereign entities, an accurate forecast for corporate credit

spread is useful for corporate and government decision‐making. The better risk prediction from our combined models

improves the pricing of credit derivatives for private traders, the measurement of corporate risk for regulatory agencies;

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