Optimal Default and Liquidation with Tangible Assets andDebt Renegotiation
Makoto Goto∗

Masaaki Kijima†

Teruyoshi Suzuki‡

Shorter Version of First Draft: May 24, 2010§

Abstract
This paper proposes a new pricing model for corporate securities issued by a levered ﬁrm
with the possibility of debt renegotiation. We take the structural approach that the ﬁrm’s
earnings follow a geometric Brownian motion with stochastic collaterals. While equity holders
can default the ﬁrm for their own beneﬁts when the earnings become insuﬃcient to go on theﬁrm, they may want to liquidate it by repaying the face value of debt to debt holders in orderto get enough residuals, when the value of collaterals becomes suﬃciently high. Unlike theexisting theoretical models, the bivariate structure enables us to distinguish strategic default,
liquidity default and the ordinary liquidation. It is shown that liquidity default and liquidation
possibly occur without entering debt renegotiation, which makes the contribution of strategic
debt service to credit spreads lower than that obtained in the previous models, irrespective of
the equity holders’ bargaining power. Our model resolves the inconsistency reported in recentempirical studies.
Keywords: Structural model; Debt renegotiation; Strategic debt service; Credit spread; Liquidity default; Strategic default; Liquidation; M&A
JEL classifications: D81; G32; G33; G35

1Introduction

The purpose of this paper is to propose a new pricing model for corporate securities issued by alevered ﬁrm with the possibility of debt renegotiation. We take the structural approach that theﬁrm’s earnings follow a geometric Brownian motion (GBM for short) with stochastic collaterals.
As in Leland (1994), equity holders can default the ﬁrm for their own beneﬁts, when the earnings
become insuﬃcient to go on the ﬁrm. In addition, equity holders may want to liquidate the ﬁrm by
repaying the face value of debt to debt holders in order to get enough residuals, when the value ofcollaterals becomes suﬃciently high. Unlike the existing structural models, the bivariate structureof our model can not only capture realistic credit spreads observed in the market, but also explain
many empirical ﬁndings reported in the literature.
There are two major approaches for the pricing of corporate securities in the ﬁnance literature.
The ﬁrst approach, called the structural approach,1 considers a ﬁrm’s asset value and deﬁnes
default as occurring either at maturity (as in Merton, 1974) or when the underlying process reaches
a default boundary for the ﬁrst time (as in Black and Cox, 1976; Brennan and Schwartz, 1984).
∗ Graduate School of Economics and Business Administration, Hokkaido University.
† Graduate School of Social Sciences, Tokyo Metropolitan University.

‡ Corresponding Author. Graduate School of Economics and Business Administration, Hokkaido University.
Address: Kita 9, Nishi 7, Kita-ku, Sapporo 060-0809, Japan. E-mail: suzuki@econ.hokudai.ac.jp§ The Full Paper is available from HUSCAP (Hokkaido University Collection of Scholarly and Academic Papers,
http://hdl.handle.net/2115/43303).
1 The other approach, called the reduced-form approach, assumes an exogenous hazard rate process as given, which
represents the likelihood of unexpected default of the ﬁrm. Major advantages of this approach are its analyticaltractability and ability of generating a ﬂexible and realistic term structure of credit spreads. However, since default
mechanism is not related to the ﬁrm value, we cannot examine the impact of ﬁrm-speciﬁc variables on the values ofcorporate securities.

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