Journal of Risk

A reduced-form contingent convertible bond model with deterministic conversion intensity

Patrick Cheridito and Zhikai Xu


The purpose of this paper is to build a contingent convertible bond (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 credit default swaps.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 2009 and Rabobank in March 2010.

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