A Reduced Form CoCo Model with Deterministic Conversion Intensity
AQR Capital Management, LLC
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 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. 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,G13working papers series
Date posted: April 21, 2013 ; Last revised: April 26, 2013
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