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A Reduced Form CoCo Model with Deterministic Conversion Intensity

13 Pages Posted: 21 Apr 2013 Last revised: 15 Mar 2015

Patrick Cheridito

ETH Zurich

Zhikai Xu

AQR Capital Management, LLC

Date Written: May 2014

Abstract

The purpose of this paper is to build a CoCo model with a minimal number of stochastic factors that includes all relevant sources of risk. The value of a CoCo stems from future coupon payments, the redemption of the principal in case the CoCo does not convert and a possible conversion into equity or cash. For calibration and hedging we propose to use the issuing firm's stock, interest rate swaps and CDS's. We model the stock price as a geometric Brownian motion with a jump at conversion. Conversion and default are assumed to occur at the first two jump times of a time-changed Poisson process. The dynamics of interest rates does not have to be specified. For pricing and calibration it is not needed, and to hedge interest rate risk one can simply immunize against the most common movements of the yield curve. A CoCo's sensitivity to conversion is described by its jump-to-default and jump-to-conversion. As case studies we analyze CoCos issued by Lloyds Banking Group in December of 2009 and Rabobank in March of 2010.

Keywords: Contingent convertible bonds, credit default swaps, reduced form model, pricing, calibration, hedging

JEL Classification: G12, G13

Suggested Citation

Cheridito, Patrick and Xu, Zhikai, A Reduced Form CoCo Model with Deterministic Conversion Intensity (May 2014). Available at SSRN: https://ssrn.com/abstract=2254403 or http://dx.doi.org/10.2139/ssrn.2254403

Patrick Cheridito (Contact Author)

ETH Zurich ( email )

Department of Mathematics
8092 Zurich
Switzerland

Zhikai Xu

AQR Capital Management, LLC

Greenwich, CT
United States

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