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Mathematical Problems in Engineering
Volume 2017, Article ID 5171470, 13 pages
https://doi.org/10.1155/2017/5171470
Research Article

First-Passage Time Model Driven by Lévy Process for Pricing CoCos

Department of Finance, Beihang University, Beijing 100191, China

Correspondence should be addressed to Xiaoshan Su; nc.ude.aaub@nahsoaixus

Received 26 July 2016; Accepted 12 December 2016; Published 11 January 2017

Academic Editor: Jean J. Loiseau

Copyright © 2017 Xiaoshan Su and Manying Bai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Contingent convertible bonds (CoCos) are typical form of contingent capital that converts into equity of issuing firm or writes down if a prespecified trigger occurs. This paper proposes a general Lévy framework for pricing CoCos. The Lévy framework indicates that the difficulty in giving closed-form expression for CoCos price is the possible introduction of the Lévy process whose first-passage time problem has not been solved. According to characteristics of new Lévy measure after the measure transform, three specific Lévy models driven by drifted Brownian motion, spectrally negative Lévy process, and double exponential jump diffusion process are proposed to give the solution keeping the form of the driving process unchanged under the measure transform. These three Lévy models provide closed-form expressions for CoCos price while the latter two possess them up to Laplace transform, whose pricing results are given by combining with numerical Fourier inversion and Laplace inversion. Numerical results show that negative jumps have large influence on CoCos pricing and the Black-Scholes model would overestimate CoCos price by simply compressing jumps information into volatility while the other two models would give more accurate CoCos price by taking jump risk into consideration.