Dynamic portfolio optimization with credit risk
File(s)
Author(s)
Jia, Longjie
Type
Thesis
Abstract
Credit risk, which considers the risk of loss resulting from a counterparty's failure to
meet contractual obligations, was not properly studied in the literature of dynamic
portfolio optimization problem until the 2008-2009 financial crisis. This thesis is
devoted to the dynamic portfolio optimization with credit risk. Two main topics
are studied in this thesis.
In the first topic, we consider a utility maximization problem with defaultable stocks
and looping contagion risk. We assume that the default intensity of one company
depends on the stock prices of itself and other companies, and the default of the
company induces immediate drops in the stock prices of the surviving companies.
Under such looping contagion risk framework, we prove that the value function is
the unique viscosity solution of the HJB equation. We also perform some numerical
tests to compare and analyse the statistical distributions of the terminal wealth of
log utility and power utility based on two strategies, one using the full information
of intensity process and the other a proxy constant intensity process. The numerical
tests confirm that modeling looping contagion risk properly is important, especially
in financial distressed period.
The second topic is on dynamic portfolio optimization with contingent convertible
(CoCo) bond. As a new type of hybrid product, CoCo bond has the interesting
feature that converting from debt to equity is contingent. We model the conversion
of CoCo bond by reduced-form approach and assume that the conversion intensity
is a deterministic function of the coupon rate and the issuing bank's stock price.
Theoretically, we construct the viscosity solution representation between the value function and the corresponding HJB equation. Practically, we compare the performance
between investing into CoCo bond and the issuing bank's stock. We analyse
the statistical distributions of terminal wealth of log utility and power utility based
on these two investment choices. Our simulation results show that, the CoCo bond
holders bear more loss than equity holders if conversion occurs. However, investing
into CoCo bond gets more profit (mean) while bearing less market risk (volatility)
as long as conversion does not occur.
meet contractual obligations, was not properly studied in the literature of dynamic
portfolio optimization problem until the 2008-2009 financial crisis. This thesis is
devoted to the dynamic portfolio optimization with credit risk. Two main topics
are studied in this thesis.
In the first topic, we consider a utility maximization problem with defaultable stocks
and looping contagion risk. We assume that the default intensity of one company
depends on the stock prices of itself and other companies, and the default of the
company induces immediate drops in the stock prices of the surviving companies.
Under such looping contagion risk framework, we prove that the value function is
the unique viscosity solution of the HJB equation. We also perform some numerical
tests to compare and analyse the statistical distributions of the terminal wealth of
log utility and power utility based on two strategies, one using the full information
of intensity process and the other a proxy constant intensity process. The numerical
tests confirm that modeling looping contagion risk properly is important, especially
in financial distressed period.
The second topic is on dynamic portfolio optimization with contingent convertible
(CoCo) bond. As a new type of hybrid product, CoCo bond has the interesting
feature that converting from debt to equity is contingent. We model the conversion
of CoCo bond by reduced-form approach and assume that the conversion intensity
is a deterministic function of the coupon rate and the issuing bank's stock price.
Theoretically, we construct the viscosity solution representation between the value function and the corresponding HJB equation. Practically, we compare the performance
between investing into CoCo bond and the issuing bank's stock. We analyse
the statistical distributions of terminal wealth of log utility and power utility based
on these two investment choices. Our simulation results show that, the CoCo bond
holders bear more loss than equity holders if conversion occurs. However, investing
into CoCo bond gets more profit (mean) while bearing less market risk (volatility)
as long as conversion does not occur.
Version
Open Access
Date Issued
2018-10
Date Awarded
2019-03
Copyright Statement
Creative Commons Attribution NonCommercial No Derivatives licence
Advisor
Zheng, Harry
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)