Related papers: Derivatives of Risk Measures
We extend the Vasi\v{c}ek loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and…
Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contains derivatives instruments. In this paper, we postpone to estimate…
We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…
Risk measures for random vectors have been considered in multi-asset markets with transaction costs and financial networks in the literature. While the theory of set-valued risk measures provide an axiomatic framework for assigning to a…
This paper investigates the impact of distributional uncertainty on key risk measures under the partial knowledge of underlying distributions characterized by their first two moments and shape information (specifically symmetry and/or…
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…
A statistically stationary and nearly homogeneous turbulent shear flow is established by an additional volume forcing in combination with stress-free boundary conditions in the shear direction. Both turbulent energy and enstrophy are…
Wrong-way risk in counterparty and funding exposures is most dramatic in the situations of systemic crises and tails events. A consistent model of wrong-way risk (WWR) is developed here with the probability-weighted addition of tail events…
In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for…
We present an original, generic, and efficient approach for computing the first and second partial derivatives of ray velocities along ray paths in general anisotropic elastic media. These derivatives are used in solving kinematic problems,…
Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…
A new semi-parametric Expected Shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of Value-at-Risk (VaR) at different…
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
Value-at-Risk (VaR) estimation at high confidence levels is inherently a rare-event problem and is particularly sensitive to tail behavior and model misspecification. This paper studies the performance of two simulation-based VaR estimation…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
The Lambda Value-at-Risk (Lambda-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk…
We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p…
Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable…