Liquidity Risk and Volatility Risk in Credit Spread Models: A Unified Approach

AuthorStylianos Perrakis,Rui Zhong
Published date01 October 2017
Date01 October 2017
Liquidity Risk and Volatility Risk in
Credit Spread Models: A Unied
Stylianos Perrakis
John Molson School of Business, Concordia University, 1455 De Maisonneuve Blvd West, Montreal
Quebec, Canada H3G 1M8
Rui Zhong
Chinese Academy of Finance and Development, Central University of Finance and Economics, P.R.
China, 39 South College Road, Haidian District, Beijing, P. R. of China, 100081
We present an integrated framework incorporating both exogenous liquidity risk in
the secondary corporate bond market and volatility risk in the dynamics of asset
value in debt rollover models. Using an innovative theoretical approach we derive
general expressions for the debt and equity values in all cases. Taking advantage of
the analytical expressions for the asset value with the constant elasticity of
variance (CEV) process, we show numerically using realistic parameter values
from empirical studies that volatility risk, together with deteriorating bond market
liquidity, decreases both debt and equity values and signicantly increases the
credit spreads.
Keywords: liquidity risk, volatility risk, credit risk, structural model
JEL classification: G12,G13,G32,G3
The authors thank John Doukas (the Editor), an anonymous referee, Jan Ericsson, Nikolay
Gospodinov, Zhiguo He, Sergey Isaenko, George Jiang, Lawrence Kryzanowski, Pascal
Francois and participants at the International Symposium on Financial Engineering and
Risk Management and 2013 Mathematical Finance Days for their valuable comments.
Financial support from the Social Sciences and Humanities Research Council (SSHRC),
National Natural Science Foundation of China (NNSFC, Project No. 71501197), the RBC
Distinguished Professorship in Financial Derivatives and the Institute of Structural Finance
and Derivatives (IFSID) is gratefully acknowledged.
European Financial Management, Vol. 23, No. 5, 2017, 873901
doi: 10.1111/eufm.12127
© 2017 John Wiley & Sons, Ltd.
1. Introduction
The credit spread of a rm is dened as the yield increment of its risky bonds over the
riskless rate. This spread primarily reects its default risk, but also other important
factors, such as the liquidity risk of the secondary bond market, the volatility risk of a
rms asset and macroeconomic conditions. The default risk has been modelled
theoretically and measured empirically in a large number of studies that are known as
structural models of the rm and follow the pioneering work of Merton (1974) and Black
and Cox (1976), which in turn were inspired by the seminal Black and Scholes (1973)
model of option pricing.
Relatively less attention has been paid to the impact of liquidity risk and volatility risk
on the credit spreads. The interaction between corporate bond market liquidity and credit
spreads was documented empirically by Longstaff et al. (2005) and Chen et al. (2007).
In Ericsson and Renault (2006) bond market illiquidity plays a role only upon default and
yields a positive correlation between illiquidity and the default components of the yield
spread. Illiquidity in the secondary bond market, however, is present whenever there is
debt renancing through rollover or other reasons, and not just upon default. Liquidity
shocks in that market are particularly serious, since the rm may not nd investors
willing to renance their debt except at a signicant cost. This issue was formally studied
by Acharya, Gale and Yorulmazer (Acharya et al. 2011), He and Xiong (HX, 2012a,b)
and He and Milbradt (2014) who showed theoretically using different models that the
liquidity risk of the secondary corporate bond market amplies the default component of
the credit spread of a rm for both exogenous and endogenous default boundaries. These
studies modeled bond market illiquidity and showed that it constitutes a frictionthat
comes from liquidation costs of the assets when the debt renancing is done by collateral
borrowing, as in the stylised two-state model of AGY, or by having the equity owners
absorb the debt rollover costs in the context of the structural models of the rm of Leland
(L, 1994b) and Leland and Toft (LT, 1996), as in HX.
Recent empirical evidence has shown that constant asset volatility does not hold in the
real world, thus motivating the study of the impact of volatility risk on credit spreads.
Perrakis and Zhong (2015) and Elkamhi et al (2013) show, respectively, that state-
dependent volatility and stochastic volatility models outperform constant volatility as in
Huang and Zhou (2008) and Huang and Huang (2012) in empirically approximating
observed credit default swap (CDS) spreads. Further, in the absence of illiquidity in the
secondary corporate debt market, Perrakis and Zhong (2015) nd that the endogenous
default boundary decreases if there is a negative relationship between asset volatility and
asset value, unlike what happens under constant volatility because of the option-like
properties of equity value. In reality, both liquidity risk and volatility risk are signicant
determinants of the default probabilities of levered rms, which in turn play a major role
in such key economic issues as the rating of a rms bonds and the valuation of its credit
derivatives such as CDS.
However, the conicting impact of liquidity risk and volatility
risk on the determinants of credit risk limits the capability of models incorporating
He and Milbradt (2014) also include frictions in the post-default bond market.
See Choi and Richardson (2009), Huang and Zhou (2008), Zhang et al. (2009), and Perrakis
and Zhong (2015).
The CDS played a major role in the 2008 nancial crisis; see Stulz (2010).
© 2017 John Wiley & Sons, Ltd.
874 Stylianos Perrakis and Rui Zhong

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