Related papers: On the Necessity of Five Risk Measures
A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a…
We analyze safety problems of complex systems using the methods of mathematical statistics for testing the output variables of a code simulating the operation of the system under consideration when the input variables are uncertain. We have…
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log…
In practice, the value-at-risk (VaR) for a longer holding period is often scaled using the 'square root of time rule'. The VaR is determined for a shorter holding period and then scaled up according to the desired holding period. For…
The Solvency II Directive and Solvency Assessment and Management (the South African equivalent) give a Solvency Capital Requirement which is based on a 99.5% Value-at-Risk (VaR) calculation. This calculation involves aggregating individual…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss…
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function…
We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…
To meet the Basel II regulatory requirements for the Advanced Measurement Approaches in operational risk, the bank's internal model should make use of the internal data, relevant external data, scenario analysis and factors reflecting the…
We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement…
By mid 2004, the Basel Committee on Banking Supervision (BCBS) is epected to launch its final recommendations on minimum capital requirements in the banking industry. Although there is the intention to arrive at capital charges which concur…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007--2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and…
This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin…