tailieunhanh - The Valuation of Convertible Bonds With Credit Risk

Convertible bonds can be difficult to value, given their hybrid nature of containing elements of both debt and equity. Further complications arise due to the frequent presence of additional options such as callability and puttability, and contractual complexities such as trigger prices and “soft call” provisions, in which the ability of the issuing firm to exercise its option to call is dependent upon the history of its stock price. This paper explores the valuation of convertible bonds subject to credit risk using an approach based on the numerical solution of linear complementarity problems. We argue that many of the existing models, such as that of Tsiveriotis. | The Valuation of Convertible Bonds With Credit Risk E. Ayache P A. Forsyth K. R. Vetzaf April 22 2003 Abstract Convertible bonds can be difficult to value given their hybrid nature of containing elements of both debt and equity. Further complications arise due to the frequent presence of additional options such as callability and puttability and contractual complexities such as trigger prices and soft call provisions in which the ability of the issuing firm to exercise its option to call is dependent upon the history of its stock price. This paper explores the valuation of convertible bonds subject to credit risk using an approach based on the numerical solution of linear complementarity problems. We argue that many of the existing models such as that of Tsiveriotis and Fernandes 1998 are unsatisfactory in that they do not explicitly specify what happens in the event of a default by the issuing firm. We show that this can lead to internal inconsistencies such as cases where a call by the issuer just before expiry renders the convertible value independent of the credit risk of the issuer or situations where the implied hedging strategy may not be self-financing. By contrast we present a general and consistent framework for valuing convertible bonds assuming a Poisson default process. This framework allows various models for stock price behaviour recovery and action by holders of the bonds in the event of a default. We also present a detailed description of our numerical algorithm which uses a partially implicit method to decouple the system of linear complementarity problems at each timestep. Numerical examples illustrating the convergence properties of the algorithm are provided. Keywords Convertible bonds credit risk linear complementarity hedging simulations Acknowledgment This work was supported by the Natural Sciences and Engineering Research Council of Canada the Social Sciences and Humanities Research Council of Canada and a subcontract with Cornell .

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