Resumen de Contribution to credit risk theory

Jorge Arturo Valverde Martínez

• This dissertation constitutes a series of contributions to the credit risk theory. Our driving problem has been that of structuring and pricing Contingency Convertible Bonds (CoCos). These recently created contingent capital instruments are converted into shares, or may suffer a principal write-down, upon the appearance of a trigger event, or contingency. CoCos have played an important role during financial crisis started in 2007.

  As part of this dissertation we have introduced a new contract, the Coupon Cancellable CoCo, which alleviates the so-called death-spiral effect exhibited by traditional CoCos. We have obtained closed-form and analytic formulas for the price of these contracts under many relevant models. In addition we have introduced the concept of extension risk and short-term uncertainty in the pricing problem when the contingency is triggered by the movements of the issuer’s share price. On the other hand, we have studied the pricing problem when modelling focus is set directly on the random time at which the contingency may occur. This led us to study of enlargements of filtrations and to the obtainment of prediction formulas for functionals of certain Lévy–driven Volterra processes. We have also study important properties of a general class of stochastic processes known as ambit processes.

  Keywords: Ambit processes; Contingency Convertible Bonds; Credit risk; Doubly stochastic Poisson processes; Enlargements of Filtrations; Lévy processes; 2