Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes
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...
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sg-ntu-dr.10356-613522023-02-28T23:31:47Z Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes Low, Kah Choon School of Physical and Mathematical Sciences Nicolas Privault Pang Zhen DRNTU::Science::Mathematics::Probability theory DRNTU::Business::Finance::Derivatives DRNTU::Engineering::Mathematics and analysis 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. Master of Science 2014-06-09T05:57:04Z 2014-06-09T05:57:04Z 2014 2014 Thesis http://hdl.handle.net/10356/61352 en 56 p. application/pdf |
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DRNTU::Science::Mathematics::Probability theory DRNTU::Business::Finance::Derivatives DRNTU::Engineering::Mathematics and analysis Low, Kah Choon Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Low, Kah Choon |
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Theses and Dissertations |
author |
Low, Kah Choon |
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Low, Kah Choon |
title |
Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
title_short |
Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
title_full |
Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
title_fullStr |
Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
title_full_unstemmed |
Valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
title_sort |
valuation of dependent defaultable bonds : stochastic analysis of determinantal point processes |
publishDate |
2014 |
url |
http://hdl.handle.net/10356/61352 |
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1759852951487119360 |