In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of the complete mixability, we provide a new lower bound for any...

This chapter reviews the recent developments of Value at Risk (VaR) estimation. In this survey, the most available univariate and multivariate methods are presented. The robustness and accuracy of these estimation methods are investigated based on the simulated and real data. In the backtesting procedure, the conditional coverage test (Christoffersen 1998), the dynamic quantile test (Engle and ...

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accords, which use value-at-risk with scenario analysis as the risk measures for setting capital requirements. We argue that a good external risk measure should be robust with respect to model misspecification and small changes in the data. A new class of data-based risk measu...

The banking systems that deal with risk management depend on underlying risk measures. Following the recommendation of the Basel II accord, most banks have developed internal models to determine their capital requirement. The Value at Risk measure plays an important role in computing this capital. In this paper we analyze in detail the errors produced by the use of this measure. We then discuss...

We discuss recent advances in the mathematical quantification of financial risk. The standard approach in terms of Value at Risk has serious deficiencies. This has motivated a systematic analysis of risk measures which satisfy some minimal requirements of coherence and consistency. Our focus will be on the basic structure theorems for convex risk measures, on the role of law-invariance, and on ...

One of the major problem faced by banks is how to manage the risk exposure in large portfolios. According to Basel II regulation banks has to measure the risk using Value-at-Risk with confidence level 99%. However, this regulation does not specify the way to calculate Valueat-Risk. The easiest way to calculate Value-at-Risk is to assume that portfolio returns are normally distributed. Altough, ...

The purpose of this paper is to review the recent derivatives security research involving liquidity risk and to summarize its implications for practical risk management. The literature supports three general conclusions. The first is that the classical option price is "on average" true, even given liquidity risk. Second, it is well known that although the classical (theoretical) option hedge ca...

Financial institutions define their marginal cost of risk on the basis of the gradients of arbitrarily chosen risk measures. We reverse this approach by calculating the marginal cost for a profit-maximizing firm with risk-averse counterparties, and then identifying the risk measure delivering the correct marginal cost. The resulting measure is a weighted average of three parts, each correspondi...

In this paper, we analyze the consequences of bank regulation on the size of the real sector. In particular, we address the question whether exogenous shocks on the return-risk characteristics of the technology and on the equity of the real sector are intensified or damped by a value-at-risk constraint on the credit portfolio of a bank. We consider a one-period model with three risk-averse agen...

Fossil energy markets have always been known as strategic and important markets. They have a significant impact on the macro economy and financial markets of the world. The nature of these markets are accompanied by sudden shocks and volatility in the prices. Therefore, they must be controlled and forecasted by using appropriate tools. This paper adopts the Generalized Auto Regressive Condition...