Credit Risk, Liquidity, and Bubbles

• Author: Philip Protter,Robert Jarrow
• DOI: http://doi.org/10.1111/irfi.12239
• Published date: 01 September 2020
• Date: 01 September 2020

Credit Risk, Liquidity, and Bubbles*

ROBERT JARROW

†,‡

AND PHILIP PROTTER

§

†

Samuel Curtis Johnson Graduate School of Management, Cornell University,

Ithaca, NY

‡

Kamakura Corporation, Honolulu, HI and

§

Statistics Department, Columbia University, New York, NY

ABSTRACT

This paper presents an arbitrage-free valuation model for a credit risky secu-

rity where credit risk coexists and interacts with an asset price bubble and

liquidity risk (or liquidity costs). As an illustration, this model is applied to

determine the fair rate for microfinance loans.

Accepted: 26 September 2018

I. INTRODUCTION

In the derivatives literature, models exist for pricing securities with credit risk

(see Jarrow 2009b for a review), liquidity risk (see Cetin et al. 2004), and asset

price bubbles (see Protter 2012 for a review). However, these risks are considered

separately. As is well known in the economics literature, these three risks coex-

ist and interact. Indeed, these interacting risks are one of the underlying causes

of financial crisis. A case in point was the 2007 credit crisis, proceeded by a

housing price bubble with expanded home loan credit risk. When the housing

bubble collapsed, massive mortgage loan defaults occurred, and a liquidity crisis

resulted (see Brunnermeier et al. 2013 for a review of the related economics

literature).

The purpose of this paper is to provide an arbitrage-free valuation model for

a credit risky security where there is also liquidity risk and an asset price bubble

is present. This valuation methodology applies to any credit risky security,

although for clarity and illustration, we will apply this model to microfinance

loans in this paper.

An outline of this paper is as follows. Section II provides the mathematical

setup of the model, and Section III provides the details of the market and the

traded securities. Section IV studies a model with credit risk and bubbles, and

Section V adds liquidity risk. Section VI applies the model to microfinance

loans, and Section VII concludes.

* Philip Protter was supported in part by NSF grant No. DMS-1612758.

© 2018 International Review of Finance Ltd. 2018

International Review of Finance, 20:3, 2020: pp. 737–746

DOI: 10.1111/irfi.12239