Pricing Vulnerable Claims in a Lévy Driven Model

45 Pages Posted: 18 Nov 2012 Last revised: 15 Feb 2014

See all articles by Agostino Capponi

Agostino Capponi

Columbia University - Department of Industrial Engineering and Operations Research

Stefano Pagliarani

DEAMS, Università di Trieste

Tiziano Vargiolu

Department of Mathematics

Date Written: February 14, 2014

Abstract

We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Levy-driven SDE. The stock jumps to zero at default with a hazard rate intensity given by a negative power of the stock price.

We recover the characteristic function of the terminal log price as the solution of a complex valued infinite dimensional system of first order ordinary differential equations.

We provide an explicit eigenfunction expansion representation of the characteristic function in a suitably chosen Banach space, and use it to price defaultable bonds and stock options. We present numerical results to demonstrate the accuracy and efficiency of the method.

Keywords: default, infinite dimensional analysis, vulnerable claims, Lévy process, characteristic function

JEL Classification: G12, G13

Suggested Citation

Capponi, Agostino and Pagliarani, Stefano and Vargiolu, Tiziano, Pricing Vulnerable Claims in a Lévy Driven Model (February 14, 2014). Finance and Stochastics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2177272 or http://dx.doi.org/10.2139/ssrn.2177272

Agostino Capponi

Columbia University - Department of Industrial Engineering and Operations Research ( email )

Stefano Pagliarani (Contact Author)

DEAMS, Università di Trieste ( email )

Via Valerio n. 4/1
Trieste
Italy

HOME PAGE: http://www.cmap.polytechnique.fr/~pagliarani/

Tiziano Vargiolu

Department of Mathematics ( email )

Italy
+390498271383 (Phone)

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