Analytic Solution to the Two Dimension Merton Model

12 Pages Posted: 12 Jul 2016 Last revised: 22 Jul 2016

See all articles by Jan Dash

Jan Dash

Fordham University; Bloomberg L.P.

Mario Bondioli

Bloomberg L.P.

Harvey J. Stein

Two Sigma; Columbia University - Department of Mathematics

Date Written: July 11, 2016

Abstract

We present an exact analytic solution to the two-dimensional correlated default structural Merton model in the form of a local volatility problem using a conformal square-root transformation of the exact solution to a 2D hybrid barrier problem. We also give an approximation and evaluate it numerically to give an example. Finally we give an exact simpler solution for the zero correlation case.

Keywords: Merton, two dimensional, local volatility, hybrid barrier, approximation, correlated default, structural, conformal

JEL Classification: C1, C14, C22, C63, E44, F65, G1, Y1

Suggested Citation

Dash, Jan and Bondioli, Mario and Stein, Harvey J., Analytic Solution to the Two Dimension Merton Model (July 11, 2016). Available at SSRN: https://ssrn.com/abstract=2808117 or http://dx.doi.org/10.2139/ssrn.2808117

Jan Dash (Contact Author)

Fordham University ( email )

113 West 60th Street
New York, NY 10023
United States

Bloomberg L.P. ( email )

731 Lexington Ave
New York, NY 10022
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Mario Bondioli

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Harvey J. Stein

Two Sigma ( email )

100 6th Ave
New York, NY 10013
United States
10013 (Fax)

Columbia University - Department of Mathematics ( email )

New York, NY
United States

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