A Dynamic Correlation Model for Pricing Credit Derivatives in A Lattice Framework
This thesis establishes a mathematical framework of the operator methods which are applied to a new dynamic correlation model extended to the class of affine reduced-form models. The proposed operator methods for lattice representations are robust and allow one to specify rich dynamic structures for the hazard rates during the portfolio credit derivative pricing. Particularly, a specific bi-variate process has been handled by the operator method to tackle the challenge of calculating joint transition probabilities for the bi-variate process. The joint generator is constructed on a two-dimensional lattice and a block-diagonalization algorithm is utilized during the computation. With the highly flexible choices of hazard structures, the proposed dynamic correlation model is capable of capturing unpredictable systematic risks observed in the crisis situation when the hazard rate processes are picked up simultaneous for all credit names within a portfolio. The model is able to capture realistic and meaningful correlations and fills the gap in applications where models from the affine class are out of reach.
bi-variate Markov process, operator method, infinitesimal generator, collateralized debt obligation, dynamic correlation, reduced-form model
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