Local Volatility Enhanced by a Jump to Default

17 Pages Posted: 28 Jan 2010 Last revised: 13 May 2010

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: January 22, 2010

Abstract

A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for GM and FORD over the period October 2004 to September 2007.

Keywords: Hazard Rates, CDS Curves, Weibull Distribution, VGSSD Sato Process

JEL Classification: G1, G12, G13

Suggested Citation

Carr, Peter P. and Madan, Dilip B., Local Volatility Enhanced by a Jump to Default (January 22, 2010). Robert H. Smith School Research Paper No. RHS 06-119. Available at SSRN: https://ssrn.com/abstract=1540874 or http://dx.doi.org/10.2139/ssrn.1540874

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

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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