Pricing vulnerable claims in a Lévy-driven model

Agostino Capponi (), Stefano Pagliarani () and Tiziano Vargiolu

Finance and Stochastics, 2014, vol. 18, issue 4, 755-789

Abstract: We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Lévy-driven SDE. The stock jumps to zero at default with a hazard rate given by a negative power of the stock price. We recover the characteristic function of the terminal log price as the solution of an infinite-dimensional system of complex-valued 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Default; Infinite-dimensional analysis; Vulnerable claims; Lévy process; Characteristic function; 60J60; 60J65; 60G70; 60G75; G12; G13 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00780-014-0239-6

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