PhD Dissertation Presentation
Title: In the Wake of the Financial Crisis – Regulators’ and Investors’ Perspectives
Abstract: Before the 2008 financial crisis, most research in financial
mathematics focused on the risk management and options' pricing
without considering effects of counterparties’ default, illiquidity
problems, systemic risk and the role of the repurchase agreement (Repo).
During the 2008 financial crisis, a frozen repo market led to a shutdown
of short sales in the stock market. Cyclical interdependencies among
corporations caused that a default of one firm seriously affected other
firms and even the whole financial network.
In this dissertation, we will consider financial markets which are shaped
by financial crisis. This will be done from two distinct perspectives, an
investor’s and a regulator’s. From an investor's perspective, recently
models were proposed to compute the total valuation adjustment (XVA)
of derivatives without considering a potential crisis in the market. In our
research, we include a possible crisis by apply an alternating renewal
process to describe a switching between a normal financial status and a
financial crisis status. We develop a framework for pricing the XVA of a
European claim in this state-dependent framework. We represent the
price as a solution to a backward stochastic differential equation and
prove the solution's existence and uniqueness.
To study financial networks from a regulator’s perspective, one popular
method is the fixed-point based approach by L. Eisenberg and T. Noe.
However, in practice, there is no accurate record of the interbank
liabilities and thus one has to estimate them to use Eisenberg and Noe
type models. In our research, we conduct a sensitivity analysis of the
Eisenberg and Noe framework, and quantify the clearing payment’s
sensitivity to such estimation errors. We show that the effect of the
missing specification of interbank connection to clearing payments can
be described via directional derivatives that can be represented as
solutions of fixed point equations. We also compute the probability of
observing clearing payment deviations of a certain magnitude.
Dr. Stephan Sturm, WPI (Advisor)
Dr. Agostino Capponi, Columbia University
Dr. Igor Cialenco, Illinois Institute of Technology
Dr. Randy Paffenroth, WPI
Dr. Gu Wang, WPI