Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes

• Main Author: Low, Kah Choon
• Other Authors: School of Physical and Mathematical Sciences
• Format: Theses and Dissertations
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics::Probability theory; DRNTU::Business::Finance::Derivatives; DRNTU::Engineering::Mathematics and analysis
• Online Access: http://hdl.handle.net/10356/61352
• Institution: Nanyang Technological University

There are two parts in this thesis where both parts are self-contained. The first part of this thesis is on the valuation of dependent defaultable bonds under the assumption that the credit risk is of a reduced-form model, where the default time is defined as a single jump process. Our work is an extension of Jarrow and Yu primary-secondary framework, where the default intensity of secondary firm is correlated with both the risk-free spot interest rate and the default of primary firm. Closed form solutions are presented for the valuation of dependent defaultable bonds under Hull-White (include Vasicek) model and CIR model. The second part is on the simulation and stochastic analysis of determinantal point processes (DPP). DPP serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in [9], which generate the perfect distribution point wise through rejection sampling. In our work, we investigate the application of perfect simulation via coupling from the past (CFTP) on DPP. We give a general framework for CFTP on DPP model. It is shown that the time-to-coalescence of the coupling is asymptotically of the order log z, where z is the initial number of configuration points of the dominating process. An application is given to the simulation of stationary models of DPP.