# Credit Risk Management and Jump Models

Diop, Sidy (2018) Credit Risk Management and Jump Models, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica, 31 Ciclo. DOI 10.6092/unibo/amsdottorato/8745.
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## Abstract

This doctoral thesis comprises three research papers that seek to improve and create corporate and sovereign credit risk models, to provide an approximate analytic expressions for CDS spreads and a numerical method for partial differential equation arisen from pricing defaultable coupon bond. First, an extension of Jump to Default Constant Elasticity Variance in more general and realistic framework is provided (see Chapter 3). We incorporate, in the model introduced in [9], a stochastic interest rate with possible negative values. In addition we provide an asymptotic approximation formula for CDS spreads based on perturbation theory. The robustness and efficiency of the method is conformed by several calibration tests on real market data. Next, under the model introduced in Chapter 3, we present in Chapter 4 a new numerical method for pricing non callable defaultable bond. we propose appropriate numerical schemes based on a Crank-Nicolson semi-Lagrangian method for time discretization combined with biquadratic Lagrange finite elements for space discretization. Once the numerical solutions of the PDEs are obtained, a post-processing procedure is carried out in order to achieve the value of the bond. Finally, we introduce a hybrid Sovereign credit risk model in which the intensity of default of a sovereign is based on the jump to default extended CEV model (see Chapter 5). The model captures the interrelationship between creditworthiness of a sovereign, its intensity to default and the correlation with the exchange rate between the bond's currency and the currency in which the CDS spread are quoted. We consider the Sovereign Credit Default Swaps Italy, during and after the financial crisis, as a case of study to show the effectiveness of our model.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Diop, Sidy
Supervisore
Co-supervisore
Dottorato di ricerca
Ciclo
31
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
credit default swap, hybrid credit-equity model, Constant Elasticity of Variance model, asymptotic expansion, Foreign exchange rate, coupon bond, default risk, PDE, semi-Lagrangian method, biquadratic Lagrange finite elements.
URN:NBN
DOI
10.6092/unibo/amsdottorato/8745
Data di discussione
15 Novembre 2018
URI