Essays in Quantitative Risk Management for Financial Regulation of Operational Risk Models

An extensive amount of evolving guidance and rules are provided to banks by financial regulators. A particular set of instructions outline requirements to calculate and set aside loss-absorbing regulatory capital to ensure the solvency of a bank. Mathematical models are typically used by banks to quantify sufficient amounts of capital. In this thesis, we explore areas that advance our knowledge in regulatory risk management.

In the first essay, we explore an aspect of operational risk loss modeling using scenario analysis. An actuarial modeling method is typically used to quantify a baseline capital value which is then layered with a judgemental component in order to account for and integrate what-if future potential losses into the model. We propose a method from digital signal processing using the convolution operator that views the problem of the blending of two signals. That is, a baseline loss distribution obtained from the modeling of frequency and severity of internal losses is combined with a probability distribution obtained from scenario responses to yield a final output that integrates both sets of information.

In the second essay, we revisit scenario analysis and the potential impact of catastrophic events to that of the enterprise level of a bank. We generalize an algorithm to account for multiple level of intensities of events together with unique loss profiles depending on the business units effected.

In the third essay, we investigate the problem of allocating aggregate capital across sub-portfolios in a fair manner when there are various forms of interdependencies. Relevant to areas of market, credit and operational risk, the multivariate shortfall allocation problem quantifies the optimal amount of capital needed to ensure that the expected loss under a convex loss penalty function remains bounded by a threshold. We first provide an application of the existing methodology to a subset of high frequency loss cells. Lastly, we provide an extension using copula models which allows for the modeling of joint fat-tailed events or asymmetries in the underlying process.