Acta academica karviniensia 2016, 16(2):95-105 | DOI: 10.25142/aak.2016.017

DETERMINATION OF VALUE AT RISK AND CONDITIONAL VALUE AT RISK BY ASSUMING ELLIPTICAL DISTRIBITION

Kateřina Zelinková1, Aleš Kresta2
1 Vysoká škola báňská-Technická univerzita Ostrava, Ekonomická fakulta, Sokolská 33, 701 21 Ostrava, Email:katerina.zelinkova@vsb.cz
2 Vysoká škola báňská-Technická univerzita Ostrava, Ekonomická fakulta, Sokolská 33, 701 21 Ostrava, Email:ales.kresta@vsb.cz

The importance of risk management is nowadays one of the most important activities of financial institutions. One of the most commonly used methods for measuring and managing market risk is the indicator of Value at Risk (the minimum predicted loss for given significant level and time horizon) and Conditional Value at Risk (the average of expected losses that exceed the value of the Value at Risk). The aim of submitted article is the estimation of Value at Risk and Conditional Value at Risk for given shares of stock's portfolio assuming elliptical distribution of probability. Significant level is determined for 15 %, 10 %, 5%, 1% and 0.5 % for time horizon one day. Firstly, fitting probability of time series will be estimated. It can be assumed that the least appropriate type of distribution for the time series will be the normal distribution. Next, VaR and CVaR will be calculated for all given probability distribution. Due to the fact that it is assumed that empirical time series and portfolio time series will correspond to either Student or Laplace distribution then the most appropriate model for estimating VaR and CVaR will be these two distributions.

Keywords: Conditional Value at Risk, Elliptical distribution, Laplace distribution, Student distribution, Value at Risk
JEL classification: G11, G24

Received: February 17, 2016; Accepted: August 24, 2016; Published: June 30, 2016  Show citation

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Zelinková K, Kresta A. DETERMINATION OF VALUE AT RISK AND CONDITIONAL VALUE AT RISK BY ASSUMING ELLIPTICAL DISTRIBITION. Acta academica karviniensia. 2016;16(2):95-105. doi: 10.25142/aak.2016.017.
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