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

43 Pages Posted: 24 Jun 2005

See all articles by Liuren Wu

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Peter Carr

New York University Finance and Risk Engineering

Date Written: September 26, 2006

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 Poisson process with a stochastic default arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a continuous process with stochastic volatility. The instantaneous default rate and instantaneous diffusion variance rate follow a bivariate continuous Markov process, with its dynamics specified to capture the empirical evidence on stock option prices and credit default swap spreads. Under this joint specification, we derive tractable pricing solutions for stock options and credit default swaps. We estimate the joint dynamics using stock option prices and credit default swap spreads for four of the most actively traded reference companies. The estimation highlights the interaction between market risk (diffusion variance) and credit risk (default arrival) in pricing stock options and credit default swaps. While the credit risk factor dominates credit spreads at long maturities, the stock return volatility also enters credit spreads at short maturities due to positive co-movements between the diffusion variance rate and the default arrival rate. Furthermore, while the diffusion variance rate influences the implied volatility uniformly across moneyness, the impact of the credit risk factor becomes much larger on options at lower strikes. The impact of the credit risk factor on stock options also increases with option maturity. For options maturing in six months, the contribution of the credit risk factor to option pricing is comparable in magnitude to the contribution of the diffusion variance rate.

Keywords: Stock options, credit default swaps, default arrival rate, return variance dynamics, option pricing, time-changed Levy processes

JEL Classification: C13, C51, G12, G13

Suggested Citation

Wu, Liuren and Carr, Peter P., Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation (September 26, 2006). Available at SSRN: https://ssrn.com/abstract=748005 or http://dx.doi.org/10.2139/ssrn.748005

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Register to save articles to
your library

Register

Paper statistics

Downloads
2,566
rank
4,625
Abstract Views
8,865
PlumX Metrics
!

Under construction: SSRN citations will be offline until July when we will launch a brand new and improved citations service, check here for more details.

For more information