The new hybrid value at risk approach based on the extreme value theory

Abstract

The new hybrid value at risk approach based on the extreme value theory* 1 El nuevo enfoque híbrido de value at risk basado en la teoría de valores extremos

Hull-White’s Value at Risk Model: Case Study of Baltic Equities Market

“…Other two models satisfied this test in all of the markets for both confidence levels. Theoretically speaking, the extreme losses, that occurre prior to and during the backtesting period, can cause high VaR estimates and this way unconditional risk coverage is automatically achieved without taking into consideration the actual market risk (Radivojevic et al 2016a). This is why, for those markets in which the models passed the Kupiec's test, it is necessary to employ the Christofferson's test of conditional coverage, noting that because of the imperfections of this test, it is possible that the model which did not satisfy the unconditional coverage test, passed the test of conditional coverage, which does not mean that the VaR estimate is valid.…”

“…Although there is a widespread agreement about the use of VaR as the general measure of market risk and the economic loss that banks and other financial institutions may suffer due to exposure to the market risk (Radivojevic et al 2016a), there is no agreement on the best model to estimate VaR. All VaR models are based on assumptions which represent a compromise between the efficiency of implementation, on the one hand, and the statistical precision of market risk estimates on the other.…”

“…These efforts have resulted in a number of models. Some of the most famous models derived from the HS model are: the BRW model proposed by Boudoukh et al (1998), filtered historical simulation proposed by Barone-Adesi et al (1998), the Mirrored historical simulation (MHS) proposed by Holton (1998), the Hybrid historical simulation model (HHS) proposed by Zikovic (2010), Dynamic historical simulation (DHS) proposed by Bee (2012), new Hybrid historical simulation model proposed by Radivojevic et al (2016a), Bootstrap historical simulation proposed by Radivojevic et al (2017), etc. The common feature of these models is that they do not behave as it would be expected based on the procedures behind the models (see Stancic et al 2013); they are computationally very intensive because they require a relatively large number of parameters that cannot be solved in a closed, analytical form and can result in negative values, where both problems have a negative influence on the maximum estimated likelihood.…”