Credit risk modelling and valuation of CoCo bonds

Abstract

[en] The main goal of this thesis is to perform a detailed introduction to credit risk modelling and then apply it to do a theoretical study of one particular reduced-form model of credit risk. The first part of this thesis is aimed to understand what credit risk is (illustrating this concept with some basic examples of credit-risk sensitive financial instruments) and to build an abstract mathematical setting under which we can model and price credit-risk sensitive instruments. In this sense, we present the well-known risk-neutral valuation formula and we discuss its validity. The second part of this thesis is an exposition of the two main approaches to model credit risk: the structural approach and the reduced-form approach. We focus on the advantages and disadvantages of each approach and we present some particular models. We also derive one useful rewrite of the risk-neutral valuation formula under the reduced-form approach and we apply it to price a credit default swap. The last part of this thesis is focused on studying the reduced-form model built in the article [2] in order to develop pricing formulas for the so-called contingent convertible bonds or CoCos. Our purpose is to describe this model by adapting it to the abstract setting and notations established in the first two parts of this thesis, to complete the proofs given in [2] by developing those details which are left to the reader and to explain how this model can be implemented in practice.