Corporate Bond Defaults: Models and Simulations
72 Pages Posted: 4 Jan 2020
Date Written: October 18, 2017
This thesis lies at the intersection of mathematics, finance and numerical methods. The financial question of how to model credit risk, specifically corporate bond defaults, and how to model correlations between defaults, motivates our study of the mathematics behind a specific kind of credit risk models called hazard rate models. We consider corporate bond defaults as random events and apply a probabilistic framework to pricing defaultable corporate bonds and to analyzing the case of multi-entity defaults and default correlations. Using the R programming language, we simulate different algorithms and discretization schemes of stochastic processes, checking our theoretical results with simulation results and numerically solving stochastic differential equations where we do not know the closed-form solutions. This motivates us to study and test performance of different simulation methods of stochastic differential equations. In the end, we give a short summary of the two other types of credit risk models as comparisons to think critically of hazard rate models so as to better answer the financial question of how to model credit risk.
Keywords: Asset Pricing, Finance
JEL Classification: G10, G12, G00, G32
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