On risk measuring in the variance-gamma model

2018 ◽  
Vol 35 (1-2) ◽  
pp. 23-33 ◽  
Author(s):  
Roman V. Ivanov
Keyword(s):  
Value At Risk ◽  
Hypergeometric Functions ◽  
Risk Measures ◽  
Random Variables ◽  
Gamma Model ◽  
Variance Gamma ◽  
Stochastic Volatilities ◽  
Investment Returns ◽  
Variance Gamma Model ◽  
Analytical Expressions

AbstractIn this paper, we discuss the problem of calculating the primary risk measures in the variance-gamma model. A portfolio of investments in a one-period setting is considered. It is supposed that the investment returns are dependent on each other. In terms of the variance-gamma model, we assume that there are relations in both groups of the normal random variables and the gamma stochastic volatilities. The value at risk, the expected shortfall and the entropic monetary risk measures are discussed. The obtained analytical expressions are based on values of hypergeometric functions.

scholarly journals Value-at-risk for the USD/ZAR exchange rate: The Variance-Gamma model

2015 ◽  
Vol 18 (4) ◽  
pp. 551-566 ◽  
Author(s):  
Lionel Establet Kemda ◽  
Chun-Kai Huang ◽  
Knowledge Chinhamu
Keyword(s):  
At Risk ◽  
Exchange Rates ◽  
Value At Risk ◽  
Financial Stability ◽  
Financial Time Series ◽  
Information Criterion ◽  
Ratio Test ◽  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model

A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale. South African exchange rates, in particular, have a significant impact on imports, inflation, consumer prices and monetary policies. Consequently, it is imperative for economists and investors to assess accurately the associated exchange risks. Exchange rates, like most financial time series, are leptokurtic and contradict the classical Gaussian assumption. We therefore introduce subclasses of the generalised hyperbolic distribution as alternative models and contrast these with the normal distribution. We conclude that the variance-gamma model is the most robust for describing the log-returns of daily USD/ZAR exchange rates and their related Value-at-Risk (VaR) estimates. The model selection methodologies utilised in our analyses include the robust Kolmogorov-Smirnov test and the Akaike information criterion. Backtesting on the adequacy of VaR estimates is also performed using the Kupiec likelihood ratio test.

OPTION PRICING IN THE VARIANCE-GAMMA MODEL UNDER THE DRIFT JUMP

2018 ◽  
Vol 21 (04) ◽  
pp. 1850018 ◽  
Author(s):  
ROMAN V. IVANOV
Keyword(s):  
Option Pricing ◽  
Drift Rate ◽  
Research Direction ◽  
Gamma Process ◽  
Gamma Model ◽  
Hyperbolic Functions ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Variance Gamma Model ◽  
Analytical Expressions

This paper continues elements of the research direction of the work of Madan et al. [(1998) The variance gamma process and option pricing, European Finance Review 2, 79–105] and gives analytical expressions for the prices of digital and European call options in the variance-gamma model under the assumption that the linear drift rate of stock log-returns can suddenly jump downwards. The time of the jump is taken to be exponentially distributed. The formulas obtained require the computation of some generalized hyperbolic functions.

scholarly journals Value-at-risk for the USD/ZAR exchange rate : the variance-gamma model

2015 ◽  
Vol 18 (4) ◽  
pp. 551-556
Author(s):  
Kemda, Lionel Establet ◽  
Huang, Chun-Kai ◽  
Chinhamu, Knowledge
Keyword(s):  
At Risk ◽  
Exchange Rate ◽  
Value At Risk ◽  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model

scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

The β-variance gamma model

2010 ◽  
Vol 14 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Wim Schoutens ◽  
Geert Van Damme
Keyword(s):  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model

scholarly journals Robustness regions for measures of risk aggregation

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Silvana M. Pesenti ◽  
Pietro Millossovich ◽  
Andreas Tsanakas
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Random Variables ◽  
Distribution Functions ◽  
Aggregation Function ◽  
Convex Risk Measures ◽  
Linear Growth Condition ◽  
Risk Aggregation ◽  
Definition Of

AbstractOne of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in the space of distribution functions, where law-invariant convex risk measures are indeed robust. Examples include the set of random variables with bounded second moment and those that are less volatile (in convex order) than random variables in a given uniformly integrable set. Typically, a risk measure is evaluated on the output of an aggregation function defined on a set of random input vectors. Extending the definition of robustness to this setting, we find that law-invariant convex risk measures are robust for any aggregation function that satisfies a linear growth condition in the tail, provided that the set of possible marginals is uniformly integrable. Thus, we obtain that all law-invariant convex risk measures possess the aggregation-robustness property introduced by [26] and further studied by [40]. This is in contrast to the widely-used, non-convex, risk measure Value-at-Risk, whose robustness in a risk aggregation context requires restricting the possible dependence structures of the input vectors.

scholarly journals Fitting the Variance-Gamma Model: A Goodness-of-Fit Check for Emerging Markets

2013 ◽  
Vol 27 (2) ◽  
pp. 1-10
Author(s):  
Ahmet Göncü ◽  
Mehmet Oğuz Karahan ◽  
Tolga Umut Kuzubaş
Keyword(s):  
Emerging Markets ◽  
Goodness Of Fit ◽  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model
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