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A Reduced Form CoCo Model with Deterministic Conversion Intensity

Patrick Cheridito

Princeton University

Zhikai Xu

AQR Capital Management, LLC; Princeton University

April 20, 2013

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 typical CoCo stems from future coupon payments, the redemption of the principal in case the CoCo does not convert and a possible conversion into equity. For calibration and hedging we propose to use the issuing fi rm'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 specifi ed. 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. To describe a CoCo's sensitivity to conversion we introduce the risk metric jump-to-conversion. As case studies we investigate CoCos issued by Lloyds Banking Group in December of 2009 and Rabobank in March of 2010.

Number of Pages in PDF File: 12

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

JEL Classification: G12,G13

working papers series

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Date posted: April 21, 2013 ; Last revised: April 26, 2013

Suggested Citation

Cheridito, Patrick and Xu, Zhikai, A Reduced Form CoCo Model with Deterministic Conversion Intensity (April 20, 2013). Available at SSRN: http://ssrn.com/abstract=2254403 or http://dx.doi.org/10.2139/ssrn.2254403

Contact Information

Patrick Cheridito (Contact Author)
Princeton University ( email )
Princeton University
Princeton, NJ 08544
United States

Zhikai Xu
AQR Capital Management, LLC
Greenwich, CT
United States
Princeton University ( email )
22 Chambers Street
Princeton, NJ 08544
United States
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