Convertible Bonds in a Defaultable Diffusion Model

Tomasz Bielecki , Stephane Crepey , Monique Jeanblanc , Marek Rutkowski


In this paper, we study convertible securities (CS) in a primary market model consisting of: a savings account, a stock underlying a CS, and an associated CDS contract (or, alternatively to the latter, a rolling CDS more realistically used as an hedging instrument). We model the dynamics of these three securities in terms of Markovian diffusion set-up with default. In this model, we show that a doubly reflected Backward Stochastic Differential Equation associated with a CS has a solution, meaning that super-hedging of the arbitrage value of a convertible security is feasible in the present set-up for both issuer and holder at the same initial cost, and we provide the related (super-)hedging strategies.
Author Tomasz Bielecki
Tomasz Bielecki,,
, Stephane Crepey
Stephane Crepey,,
, Monique Jeanblanc
Monique Jeanblanc,,
, Marek Rutkowski ZPSMF
Marek Rutkowski,,
- Department of Stochastic Processes and Financial Mathematics
Book Stochastic Analysis with Financial Applications, Progress in Probability, vol. 65, 2011, ISBN 978-3-0348-0096-9
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Citation count*0 (2015-05-30)
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