Faculty Advisor or Committee Member

Gu Wang, Committee Member

Faculty Advisor or Committee Member

Randy Paffenroth, Committee Member

Faculty Advisor or Committee Member

Igor Cialenco, Committee Member

Faculty Advisor or Committee Member

Agostino Capponi, Committee Member

Faculty Advisor or Committee Member

Stephan Sturm, Advisor

Identifier

etd-042319-143631

Abstract

Before the 2008 financial crisis, most research in financial mathematics focused on the risk management and the pricing of options 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 financial 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 existence and uniqueness of the solution. 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 - Noe type models. In our research, we conduct a sensitivity analysis of the Eisenberg - Noe framework, and quantify the effect of the estimation errors to the clearing payments. 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.

Publisher

Worcester Polytechnic Institute

Degree Name

PhD

Department

Mathematical Sciences

Project Type

Dissertation

Date Accepted

2019-04-23

Accessibility

Unrestricted

Subjects

arbitrage pricing, backward stochastic differential equations, contagion, Eisenberg–Noe clearing vector, financial crisis, interbank networks, option pricing, sensitivity analysis, systemic risk, value adjustments

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