Article2008

DEFAULTABLE OPTIONS IN A MARKOVIAN INTENSITY MODEL OF CREDIT RISK

Tomasz R. Bielecki · Stéphane Crépey · Monique Jeanblanc · Marek Rutkowski

42 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Corporate Insolvency and Governance Credit Risk and Financial Regulations

Abstract

This paper is a follow‐up to “Valuation and Hedging of Defaultable Game Options in a Hazard Process Model” by the same authors. In the present paper we give user friendly assumptions ensuring that the general conditions in the previous paper are satisfied. We also give a systematic procedure to construct suitable intensity models of credit risk, and, in the Markovian case, we provide a variational inequality approach to the pre‐default pricing problem. We finally illustrate our results on a study of defaultable convertible bonds.

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References

2005Stochastic Integration and Differential Equations 2003Limit Theorems for Stochastic Processes 1997Backward Stochastic Differential Equations in Finance 1979Calcul Stochastique et Problèmes de Martingales 2004Credit Risk: Modeling, Valuation and Hedging 1998The fundamental theorem of asset pricing for unbounded stochastic processes 2007Forward-Backward Stochastic Differential Equations and their Applications 1996Backward stochastic differential equations with reflection and Dynkin games

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2009BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game 2009Defaultable Game Options in a Hazard Process Model 2011Convertible Bonds in a Defaultable Diffusion Model 2014Second-order BSDEs with general reflection and game options under uncertainty

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