In the Wake of the Financial Crisis - Regulators’ and Investors’ Perspectives

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

Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often estimate this matrix because complete information on bilateral liabilities is rarely available. As a result, the clearing vector may suffer from estimation errors in the liabilities matrix. We quantify the clearing vector's sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. This allows us to compute upper bounds for the worst case perturbations of the clearing vector in our simple setting. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix. Applying our methodology to a dataset of European banks, we find that perturbations to the relative liabilities can result in economically sizeable differences that could lead to an underestimation of the risk of contagion. Our results are a first step towards allowing regulators to quantify errors in their simulations.Comment: 37 page

The Interplay between COVID-19 and the Economy in Canada

We propose a generalized susceptible-exposed-infected-removed (SEIR) model to track COVID-19 in Canadian provinces, taking into account the impact of the pandemics on unemployment. The model is based on a network representing provinces, where the contact between individuals from different locations is defined by a data-driven mixing matrix. Moreover, we use time-dependent parameters to account for the dynamical evolution of the disease incidence, as well as changes in the rates of hospitalization, intensive care unit (ICU) admission, and death. Unemployment is accounted for as a reduction in the social interaction, which translates into smaller transmission parameters. Conversely, the model assumes that higher proportions of infected individuals reduce overall economic activity and therefore increase unemployment. We tested the model using publicly available sources and found that it is able to reproduce the reported data with remarkable in-sample accuracy. We also tested the model’s ability to make short-term out-of-sample forecasts and found it very satisfactory, except in periods of rapid changes in behavior. Finally, we present long-term predictions for both epidemiological and economic variables under several future vaccination scenarios

Direct Probability Integral Method for Seismic Performance Assessment of Earth Dam Subjected to Stochastic Mainshock–Aftershock Sequences

Studying the impact of mainshock–aftershock sequences on dam reliability is crucial for effective disaster prevention measures. With this purpose in mind, a new method for stochastic dynamic response analyses and reliability assessments of dams during seismic sequences has been proposed. Firstly, a simulation method of stochastic seismic sequences is described, considering the dependence between mainshock and aftershock based on Copula function. Then, a novel practical framework for stochastic dynamic analysis is established, combined with the improved point selection strategy and the direct probability integration method (DPIM). The DPIM is employed on a nonlinear system with one degree of freedom and compared with Monte Carlo simulation (MCS). The findings reveal that the method boasts exceptional precision and efficiency. Finally, the seismic performance of a practical dam was evaluated based on the above method, which not only accurately estimates the response probability distribution and dynamic reliability of the dam, but also greatly reduces the required calculations. Furthermore, the impact of aftershocks on dam seismic performance is initially evaluated through a probability approach in this research. It is found that seismic sequences will significantly increase the probability of earth dam failure compared with sequences of only mainshocks. In addition, the influence of aftershocks on reliability will further increase when the limit state is more stringent. Specifically, the novel analysis method proposed in this paper provides more abundant and objective evaluation indices, providing a dynamic reliability assessment for dams that is more effective than traditional evaluation methods

Facile Route for Bio-Phenol Siloxane Synthesis via Heterogeneous Catalytic Method and its Autonomic Antibacterial Property

Eugenol, used as bio-phenol, was designed to replace the hydrogen atom of hydrogenterminated siloxane by hydrosilylation reaction under the presence of alumina-supported platinum catalyst (Pt-Al2O3), silica-supported platinum catalyst (Pt-SiO2) and carbon nanotube-supported platinum catalyst (Pt-CNT), respectively. The catalytic activities of these three platinum catalysts were measured by nuclear magnetic resonance hydrogen spectrometer (1H NMR). The properties of bio-phenol siloxane were characterized by Fourier transform infrared spectrometer (FT–IR), UV-visible spectrophotometer (UV) and thermogravimeter (TGA), and its antibacterial property against Escherichia coli was also studied. The results showed that the catalytic activity of the catalyst Pt-CNT was preferable. When the catalyst concentration was 100 ppm, the reaction temperature was 80 °C and reaction time was 6 h, the reactant conversion rate reached 97%. After modification with bio-phenol, the thermal stability of the obtained bio-phenol siloxane was improved. For bio-phenol siloxane, when the ratio of weight loss reached 98%, the pyrolysis temperature was raised to 663 °C which was 60 °C higher than hydrogenterminated siloxane. Meanwhile, its autonomic antibacterial property against Escherichia coli was improved significantly