In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...

We study Aumann and Serrano's (2008) risk index for sums of gambles that are not dependent. If the dependent parts are similarly ordered, then the risk index of the sum is always larger than the minimum of the risk indices of the two gambles. For negative dependence, the risk index of the sum is...

This teaching note provides step-by-step instruction for simulating the net present value and the internal rate of return of a five-year project. The uncertainty lie in the initial level of sales, sales growth rates, gross profit margins, operating expenses before depreciation, and the terminal...

It is important to incorporate diverse heavy-tailed dependency between risks in estimating economic capital. Copulas can be a useful technique to capture dependence structure where extreme events occur simultaneously. Using the sample of U.S. property liability insurance industry, we examine the...

It is well known that a plain riskless floater is worth par and has zero interest rate delta immediately before a fixing in a classic one curve setup. We investigate the structure of the delta under credit risk, a first fixing and a margin added to the payoff. We decompose the delta into three...

A framework which consistently and fully integrates market, credit and country transfer risks of a general portfolio of financial assets in a multi-period setup is developed. An appropriate definition of exposure, loss-given-defaults and loss-given-transfer-events provides a unified treatment of...

This paper analyses and develops insights to systematic risk and diversification when random, imperfectly dependent, losses are aggregated. Systematic risk and diversification are shown to vary across layers of component losses according to local dependence and volatility structures. Systematic...

We provide an extreme value analysis of the returns of Bitcoin. A particular focus is on the tail risk characteristics and we will provide an in-depth univariate extreme value analysis. Those properties will be compared to the traditional exchange rates of the G10 currencies versus the US...

In this work, we have found a risk model that improves the performance of Risk Targeting. Risk Targeting in portfolio construction is implemented to improve capital utilization in growing markets and systematically step away from risk scenarios. However, the performance of risk targeting varies...

To avert the impending global Cyber-Finance Insurance Crisis based upon large-scale commercial reliance upon quantitative models with inherent model risks, tail risks, and systemic risks in current form, this post-doctoral thesis makes the following key contributions: Develops the first known...