Equity Option Implied Probability of Default and Equity Recovery Rate

• Published date: 01 June 2017
• DOI: http://doi.org/10.1002/fut.21823
• Date: 01 June 2017
• Author: Bo Young Chang,Greg Orosi

Equity Option Implied Probability of

Default and Equity Recovery Rate

Bo Young Chang and Greg Orosi*

There is a close link between prices of equity options and the default probability of a firm.

We show that in the presence of positive expected equity recovery, standard methods that

assume zero equity recovery at default misestimate the option-implied default probability. We

introduce a simple method to detect stocks with positive expected equity recovery by examining

option prices and propose a method to extract the default probability from option prices that

allows for positive equity recovery. We demonstrate possible applications of our methodology

with examples that include financial institutions in the United States during the 2007–09

subprime crisis. ©2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:599–613, 2017

1. INTRODUCTION

There is a long line of literature linking option pricing models with the probability of default

of a firm, following the seminal work by Merton (1974). Most of the studies in this literature

(e.g., Bayraktar & Yang, 2011; Carr & Linetsky, 2006; Carr & Madan, 2010; Carr & Wu,

2009; and Linetsky, 2006) assume that there is no residual asset left to pay equity investors

in the event of a firm’s default. That is, the stock price goes to zero when a default occurs.

In most cases, the assumption of zero equity recovery at default is valid. However, in some

instances, there is significant residual value to equity investors even after a firm defaults.

To file for bankruptcy, a company is supposed to be insolvent, with debts exceeding

assets. As debt holders must be paid back before shareholders, typically firms do not have

residual funds to pay equity holders. However, some firms end up in Chapter 11 bankruptcy,

not because they are insolvent, but because they cannot get new loans or refinance existing

debt. Furthermore, for various strategic reasons, both equity holders and debt holders have

incentives to induce bankruptcy well before the equity value reaches zero.1

Bo Young Chang is at the Bank of Canada, 234 Laurie Ave. West, Ottawa, Ontario, Canada. Greg Orosi

is the Associate Professor at Department of Mathematics and Statistics, American University of Sharjah,

Sharjah, UAE. Wethank Robert Webb (Editor), the anonymous referee, Kwangil Bae, Narayan Bulusu, Peter

Christoffersen, Bruno Feunou, Jean-S´

ebastien Fontaine, Jos´

e Da Fonseca, Jun Yang, as well as participants at

the Bank of Canada Fellowship Learning Exchange, Quantitative Methods in Finance Conference, Auckland

Centre for Financial Research Derivative Markets Conference, and the Annual Conference of the Asia-Pacific

Association of Derivatives for helpful comments and suggestions.

JEL Classification: G13

*Correspondence author,Department of Mathematics and Statistics, American University of Sharjah, Office: Nab

254, P.O.Box 26666, Sharjah, UAE, Tel: 971-6-515-2332, Fax: 971-6-515-2950, e-mail: gorosi@aus.edu.

Received December 2015; Accepted September 2016

1See Broadie, Chernov,and Sundaresan (2007); Davydenko (2012); Fan and Sundaresan (2000); Hackbarth, Hen-

nessy, and Leland (2007); Leland (1994); and Leland and Toft (1996)

The Journal of Futures Markets, Vol. 37, No.6, 599–613 (2017)

©2016 Wiley Periodicals, Inc.

Published online 9 November 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21823