Endogenous Credit Spreads and Optimal Debt Financing Structure in the Presence of Liquidity Risk

AuthorEva Lütkebohmert,Daniel Oeltz,Yajun Xiao
Date01 January 2017
Published date01 January 2017
Endogenous Credit Spreads and
Optimal Debt Financing Structure in
the Presence of Liquidity Risk
Eva L
Department of Quantitative Finance, University of Freiburg, Platz der Alten Synagoge, 79098
Freiburg, Germany
E-mail: eva.luetkebohmert@nance.uni-freiburg.de
Daniel Oeltz
RIVACON GmbH, Im Apfelgrund 4, 61381 Friedrichsdorf, Germany
E-mail: d.oeltz@rivacon.com
Yajun Xiao
Business School, University of Technology Sydney, PO Box 123 Broadway, NSW 2007 Sydney,
E-mail: Yajun.Xiao@uts.edu.au
We present a structural model that allows a rm to effectively manage its exposure
to both insolvency and illiquidity risk inherent in its nancing structure. Besides
insolvency risk, the rm is exposed to rollover risk through possible runs by short-
term creditors. Moreover, asset price volatilities are subject to macroeconomic
This work was supported by the Excellence Initiative through the project Pricing of Risk in
Incomplete Marketswithin the Institutional Strategy of the University of Freiburg as well
as by the German Research Foundation through the project Modelling of Market, Credit-
and Liquidity Risks in Fixed-Income Markets. The financial support is gratefully
acknowledged by the first and the third author. Several helpful comments and suggestions
from Rama Cont, Damir Filipovic, Paul Glasserman, Xue-Zhong He, Gechun Liang and
Lakshithe Wagalath are very much appreciated. The authors also thank the participants at
the IMA Conference on Mathematics in Finance in Edinburgh 2013, at the Conference on
Current Topics in Mathematical Finance in Vienna 2013, at the Conference of the French
Finance Association in Lyon 2013, and at the 8
World Congress of the Bachelier Finance
Society 2014 in Brussels for several valuable remarks. Moreover, the authors are grateful to
Frank Koster for sharing his knowledge on the discretisation scheme of the Heston process
and on least square Monte Carlo methods in general. His suggestions and remarks were
highly valuable for the implementation of an efficient scheme to simulate the proposed
model. Finally, the authors would like to thank the Editor John Doukas and two anonymous
referees for valuable comments and suggestions that helped to significantly improve the
paper. Correspondence: Eva L
European Financial Management, Vol. 23, No. 1, 2017, 5586
doi: 10.1111/eufm.12089
© 2016 John Wiley & Sons, Ltd.
shocks and inuence creditorsrisk attitudes and margin requirements. Credit
spreads are derived endogenously depending on the rms total default risk. Equity
holders have to bear the rollover losses. An optimal debt structure that maximises
the rms equity value is determined by trading off lower nancing costs and
higher rollover risk.
Keywords: funding liquidity, optimal capital structure, rollover risk, structural
credit risk models
JEL classification: G01, G32, G33
1. Introduction
Heavy reliance on short-term nancing, liquidity dry-ups in the short-term debt market
and creditorspanic runs were among the major reasons of the various rm failures
during the 2007/2008 nancial crisis.
Since then there has been extensive research into
how liquidity dry-ups in the short-term lending market can lead to spiking credit spreads
and ultimately can cause rm failures. The question of how a rm can quantify and
practically cope with the risks inherent in short-term nancing has been discussed much
less. This, however, is a prevailing issue, especially as, in the aftermath of the crisis,
nancial institutions surprisingly again increase reliance on short-term nancing
This article proposes a comprehensive and tractable model that takes into account
insolvency risk, illiquidity risk associated with a rms debt structure, and potential
interactions between both sources of risk. The paper has four major contributions.
Firstly, we study the effect of both insolvency and illiquidity risk on short-term credit
spreads which are determined endogenously in our setting. When the rm is in distress,
investors will be more pessimistic and the rm needs to offer higher coupon rates to
induce them to roll over their funding. In this way, our model reects the empirically
observed fact that spreads on short-term debt increase when funding liquidity tightens.
Moreover, by investigating the effect of market deteriorations on a rms credit spread,
our paper contributes to explaining the ight-to-quality observable during the nancial
crisis of 2007/2008. Secondly, our approach allows us to study how a rmsnancing
structure affects its default probability. The more the rm relies on short-term funding,
the higher is its default probability as rolling over short-term debt becomes more
sensitive to uctuations of the rms asset value and its volatility.
In this way, our model can pr ovide valuable insights in to a rms internal risk
management, especially as feedback effects of changing cred it spreads on the rms
solvency situation are taken into ac count. Thirdly, the model allows us to det ermine a
rms optimal debt nancing struct ure, i.e., its optimal rat io of short- to long-term
debt. When short-term rate s increase, equity holders have to bear the rollover losses
subject to their limited li ability. Short-term nan cing is attractive as it is usually
In fact, it has been shown in Adrian and Shin (2008, 2010) that the use of very short-term
nancing dramatically increased during the nancial crisis of 2007/2008 and the period
immediately before that. Gorton and Metrick (2012) and Brunnermeier (2009) provide
further evidence that debt runs were one of the main reasons for the crisis.
© 2016 John Wiley & Sons, Ltd.
56 Eva L
utkebohmert, Daniel Oeltz and Yajun Xiao
cheaper than long-term nancing. However, the more a rm relies on short-term
funding, the higher is its exposu re to rollover risk. Our results sh ow that equity value
can be maximised by trading of f benets and costs associat ed with short-term
nancing. Thereby the ratio of sh ort- to long-term debt is optimi sed. Finally, our
model allows us to study the feedbac k effects of external macroe conomic shocks on
arms internal funding liquidity. I n this way, our approach can contrib ute to the
construction of efcient rules on rmsbalance sheets that can help to prevent
the emergence of liquidity spir als and hence yields valuable impl ications for the
construction of regulato ry guidelines.
Our paper is related to several st reams of literature. In the red uced-form approaches
of Longstaff et al. (2005) and Filipovic and Trol le (2013), the default rate and the
liquidity rate are exogenous processes which are independent of each other. Thes e are
converted into individual credit spread components co rresponding to default a nd
liquidity risk, respective ly. In stark contrast to this ap proach, our paper studies the
intertwined effect between insol vency and illiquidity risk. Th erefore, we build on
the structural credit risk mod el of Black and Cox (1976) where a default happens when
the rm fundamental value falls bel ow an exogenous default barr ier. We incorporate
funding liquidity risk in thi s setting by modelling creditorsrollover decisio ns at short-
term debt maturities. In our model the decision faced by short-term creditors of
whether to roll over or to withd raw their funding depends o n both future insolvency
risk and creditorsbeliefs about future debt runs. Liquidit y risk resulting from the
binary rollover decision f ollowing creditorscoordi nation is determined in par tial
equilibrium. In this regar d our approach differs consi derably from Ericsson and
Renault (2006), He and Xion g (2012b), and He and Milbrad t (2014), who employ the
framework of Leland and Toft (199 6) and introduce an exogenous liquidity shock. The
assumed staggered debt stru cture which implies stabl e coupon rates over time as wel l
as the assumption that liqu idity shocks are exogenous, allows the authors to
endogenously determine the d efault barrier which is not possi ble in our setting. It has
been documented, however , that the spread on many short- term nancing instruments
climbed dramatically duri ng the nancial crisis, whic h makes the assumption of
constant coupon rates disputab le when the average debt maturity is not lar ge.
Therefore, we allow the coupo n rate on short-term debt to vary over tim e. Thus,
instead of endogenising the defau lt barrier, in this paper we endoge nously determine
the coupon rate such that the rm can react to ch anging market conditions and p revent
creditors from running by a ppropriately adjusting t he coupon rate on short-term debt.
In He and Milbradt (2014) an d He and Xiong (2012b) rollo ver costs are exogenous
and have to be absorbed by equity hol ders. In our model, equity hol ders also need to
absorb rollover costs, howev er, these are endogenous as t hey are caused by increasing
short-term risk premia. Thi s allows us to analyse the optim al ratio of short-term debt
to long-term debt that max imises the rms equity value.
Further, our model is relevant to the bank run literature. The classical bank run models
of Bryant (1980), Diamond and Dybvig (1983) and Rochet and Vives (2004) provide
evidence for the fact that bank runs can occur as a result of coordination problems among
short-duration depositorsrollover decisions. These static models have been extended to
dynamic coordination problems in Guimaraes (2006) and He and Xiong (2012a). In
Morris and Shin (2010) the authors focus on a two-period setting where short-term
creditors face a binary decision in terms of global games at an interim time point. Liang
et al. (2014, 2015) combine ideas of global games with the dynamic coordination
© 2016 John Wiley & Sons, Ltd.
Endogenous Credit Spreads and Optimal Debt Financing 57

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