Value-at-risk and related measures for the Bitcoin

2018 ◽  
Vol 19 (2) ◽  
pp. 127-136 ◽  
Author(s):  
Stavros Stavroyiannis
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Capital Allocation ◽  
Capital Requirements ◽  
Spot Price ◽  
Content Type ◽  
Type Iv ◽  
Pearson Type ◽  
Standard And Poor's

Purpose The purpose of this paper is to examine the value-at-risk and related measures for the Bitcoin and to compare the findings with Standard and Poor’s SP500 Index, and the gold spot price time series. Design/methodology/approach A GJR-GARCH model has been implemented, in which the residuals follow the standardized Pearson type-IV distribution. A large variety of value-at-risk measures and backtesting criteria are implemented. Findings Bitcoin is a highly volatile currency violating the value-at-risk measures more than the other assets. With respect to the Basel Committee on Banking Supervision Accords, a Bitcoin investor is subjected to higher capital requirements and capital allocation ratio. Practical implications The risk of an investor holding Bitcoins is measured and quantified via the regulatory framework practices. Originality/value This paper is the first comprehensive approach to the risk properties of Bitcoin.

scholarly journals Market Risk Measurement

2020 ◽  
Author(s):  
Emese Lazar ◽  
Ning Zhang
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Preliminary Analysis ◽  
Risk Measures ◽  
Market Risk ◽  
Capital Requirements ◽  
Risk Measurement ◽  
Regulatory Framework ◽  
Bank Capital ◽  
Bank Capital Requirements

This chapter presents a preliminary analysis on how some market risk measures dramatically increased during the COVID-19 pandemic, with measures computed over longer horizons experiencing more pronounced effects. We provide examples when regulatory market risk measurement proved to be suboptimal, overestimating risk. A further issue was the large number of Value-at-Risk ‘exceptions’ during the first few months of the crisis, which normally leads to overinflated bank capital requirements. The current regulatory framework should address these problems by suggesting improvements to the calculation of risk measures and/or by modifying the rules which determine capital requirements to make them appropriate and realistic in crisis situations.

Econometric modeling and value-at-risk using the Pearson type-IV distribution

2012 ◽  
Vol 22 ◽  
pp. 10-17 ◽  
Author(s):  
S. Stavroyiannis ◽  
I. Makris ◽  
V. Nikolaidis ◽  
L. Zarangas
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Econometric Modeling ◽  
Type Iv ◽  
Pearson Type ◽  
Pearson Type Iv

Value-at-risk for the long and short trading position with the Pearson type-IV distribution

2013 ◽  
Vol 15 (1) ◽  
pp. 14 ◽  
Author(s):  
Stavros Stavroyiannis ◽  
Ilias Makris ◽  
Vasilis Nikolaidis ◽  
Leonidas Zarangas
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Type Iv ◽  
Pearson Type ◽  
Pearson Type Iv

Modelling random vectors of dependent risks with different elliptical components

2021 ◽  
pp. 1-19
Author(s):  
Zinoviy Landsman ◽  
Tomer Shushi
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Risk Measures ◽  
Capital Allocation ◽  
Risk Capital ◽  
Dependent Risks ◽  
Risk Capital Allocation ◽  
Elliptical Copula ◽  
T Distribution

Abstract In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.

scholarly journals Avaliação de Modelos de Cálculo de Exigência de Capital para Risco Cambial

2005 ◽  
Vol 3 (2) ◽  
pp. 223
Author(s):  
Claudio H. da S. Barbedo ◽  
Gustavo S. Araújo ◽  
João Maurício S. Moreira ◽  
Ricardo S. Maia Clemente
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Value At Risk ◽  
Hybrid Approach ◽  
Capital Allocation ◽  
Capital Requirements ◽  
Internal Models ◽  
Capital Requirement ◽  
Brazilian Legislation ◽  
Historical Model

This paper examines capital requirement for financial institutions in order to cover market risk stemming from exposure to foreign currencies. The models examined belong to two groups according to the approach involved: standardized and internal models. In the first group, we study the Basel model and the model adopted by the Brazilian legislation. In the second group, we consider the models based on the concept of value at risk (VaR). We analyze the single and the double-window historical model, the exponential smoothing model (EWMA) and a hybrid approach that combines features of both models. The results suggest that the Basel model is inadequate to the Brazilian market, exhibiting a large number of exceptions. The model of the Brazilian legislation has no exceptions, though generating higher capital requirements than other internal models based on VaR. In general, VaR-based models perform better and result in less capital allocation than the standardized approach model applied in Brazil.

scholarly journals Out of sample value-at-risk and backtesting with the standardized pearson type-IV skewed distribution

2013 ◽  
Vol 60 (2) ◽  
pp. 231-247 ◽  
Author(s):  
Stavros Stavroyiannis ◽  
Leonidas Zarangas
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Skewed Distribution ◽  
Financial Analyst ◽  
Type Iv ◽  
Pearson Type ◽  
Out Of Sample ◽  
Sample Testing ◽  
T Distribution ◽  
Pearson Type Iv

This paper studies the efficiency of an econometric model where the volatility is modeled by a GARCH (1,1) process, and the innovations follow a standardized form of the Pearson type-IV distribution. The performance of the model is examined by in sample and out of sample testing, and the accuracy is explored by a variety of Value-at-Risk methods, the success/failure ratio, the Kupiec-LR test, the independence and conditional coverage tests of Christoffersen, the expected shortfall measures, and the dynamic quantile test of Engle and Manganelli. Overall, the proposed model is a valid and accurate model performing better than the skewed Student-t distribution, providing the financial analyst with a good candidate as an alternative distributional scheme.

Risk measures computation by Fourier inversion

2017 ◽  
Vol 18 (1) ◽  
pp. 76-87 ◽  
Author(s):  
Ngoc Quynh Anh Nguyen ◽  
Thi Ngoc Trang Nguyen
Keyword(s):  
At Risk ◽  
Fourier Transform ◽  
Characteristic Function ◽  
Value At Risk ◽  
Risk Model ◽  
Risk Measures ◽  
Risk Measure ◽  
Efficient Computation ◽  
Fourier Inversion ◽  
Content Type

Purpose The purpose of this paper is to present the method for efficient computation of risk measures using Fourier transform technique. Another objective is to demonstrate that this technique enables an efficient computation of risk measures beyond value-at-risk and expected shortfall. Finally, this paper highlights the importance of validating assumptions behind the risk model and describes its application in the affine model framework. Design/methodology/approach The method proposed is based on Fourier transform methods for computing risk measures. The authors obtain the loss distribution by fitting a cubic spline through the points where Fourier inversion of the characteristic function is applied. From the loss distribution, the authors calculate value-at-risk and expected shortfall. As for the calculation of the entropic value-at-risk, it involves the moment generating function which is closely related to the characteristic function. The expectile risk measure is calculated based on call and put option prices which are available in a semi-closed form by Fourier inversion of the characteristic function. We also consider mean loss, standard deviation and semivariance which are calculated in a similar manner. Findings The study offers practical insights into the efficient computation of risk measures as well as validation of the risk models. It also provides a detailed description of algorithms to compute each of the risk measures considered. While the main focus of the paper is on portfolio-level risk metrics, all algorithms are also applicable to single instruments. Practical implications The algorithms presented in this paper require little computational effort which makes them very suitable for real-world applications. In addition, the mathematical setup adopted in this paper provides a natural framework for risk model validation which makes the approach presented in this paper particularly appealing in practice. Originality/value This is the first study to consider the computation of entropic value-at-risk, semivariance as well as expectile risk measure using Fourier transform method.

scholarly journals Sharing Risk – An Economic Perspective

2009 ◽  
Vol 39 (2) ◽  
pp. 591-613 ◽  
Author(s):  
Andreas Kull
Keyword(s):  
Value At Risk ◽  
Risk Sharing ◽  
Risk Measures ◽  
Insurance Industry ◽  
Risk Measure ◽  
Capital Allocation ◽  
Risk Capital ◽  
Risk Class ◽  
Capital Costs ◽  
Risk Transfer

AbstractWe revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

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