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Journal of Financial Econometrics Advance Access published online on July 21, 2009
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbp010
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org

Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation

Peter Carr
     Bloomberg LP and New York University

Liuren Wu
     Baruch College, CUNY

Address correspondence to Liuren Wu, Zicklin School of Business, Baruch College, One Bernard Baruch Way, B10-225, New York, NY 10010, or e-mail: liuren.wu{at}baruch.cuny.edu

JEL Classification: C13, C51, G12, G13


  Abstract

We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Cox process with a stochastic arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a jump-diffusion process with stochastic volatility. The instantaneous default rate and variance rate follow a bivariate continuous process, with its joint dynamics specified to capture the observed behavior of stock option prices and credit default swap spreads. Under this joint specification, we propose a tractable valuation methodology for stock options and credit default swaps. We estimate the joint risk dynamics using data from both markets for eight companies that span five sectors and six major credit rating classes from B to AAA. The estimation highlights the interaction between market risk (return variance) and credit risk (default arrival) in pricing stock options and credit default swaps.

KEYWORDS: credit default swaps, default arrival rate, option pricing, return variance dynamics, stock options, time-changed Lévy processes

We thank George Tauchen (the editor), the associate editor, two anonymous referees, Gurdip Bakshi, Philip Brittan, Bjorn Flesaker, Dajiang Guo, Pat Hagan, Harry Lipman, Bo Liu, Sheikh Pancham, Louis Scott, and participants at Bloomberg, Baruch College, MIT, the 2005 Credit Risk Conference at Wharton, the 13th annual conference on Pacific Basin Finance, Economics, and Accounting at Rutgers University, the 2006 North American Winter Meeting of the Econometric Society at Boston, and the Credit Derivative Symposium at Fordham University, for comments. Liuren Wu acknowledges partial financial support from Baruch College, The City University of New York.

Received January 22, 2009; revised May 8, 2009; accepted June 1, 2009


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