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Initially, the VaR has been anticipating to quantify the available risks in derivatives markets, but it has grown widely and it has now been applied in measuring all kinds of risks, primarily credit and market risks. It also developed from a tool that quantifies risk to a tool that is applied in active risk management. Today VaR has shifted beyond application in financial institutions. In the beginning, companies with largely exposed to financial markets used other kinds of activities before spreading to other businesses. Today, an ever-growing numbers of individual businesses apply and appreciate VaR as an effective tool for quantifying financial risksKrause (2003). This trend is evidently ...view middle of the document...

Since the true probability circulation is not well known in general, it has to be evaluated from the data. A good evaluation of the minor tail of the distribution is of crucial importance for the VaR evaluation. The obstacle comes from the fact that from the definition, only few remarks are made at the tails. This enlarges the estimation errorsKrause (2003).

On the other hand, VaR applies to several financial instruments and it is stated in similar unit of quantifying, that is, in “lost money”. On the converse, Greeks are measures created ad hoc for precise instruments or risk variables and are stated in deterrent units. The contrast of comparative riskiness between, say, a forex portfolio, and an equity portfolio is not simple with Greeks, whilst it is a straight contrast knowing their VaR’s. Secondly, VaR includes an educated guess of potential events and allows one to change in a solitary number the risk of a collection. On the contrary, Greeks essentially add up to “what if” variables Acerbi, et al (2008).

In real scenarios, due to the intricacy of computational features and to the fragility of the approximation of market possibilities, in order to calculate VaR one has to choose (sometimes strong) hypothesis both on the practical reliance of financial instruments from peril drivers (ﬁrst and second order estimates . . .) and on the distributions (past VaR, parametric VaR . . .). Sometimes it is practical to decouple the risks related to diverse risk drivers. VaR can be then calculated “switching on” some category of risk drivers, keeping all the remaining constant. One then talks of partial VaR’s like “Forex VaR” (FXVaR), “Interest Rate VaR” (IRVaR), and “Credit VaR” (CVaR)

(EQVaR), “Equity VaR”, and so onAcerbi, et al (2008).

In the case of composite portfolios uncovered to many risk erratic like in ﬁnancial institutions, the calculation of VaR can frequently be an alarming task. A demanding feature is due to a fact that the calculation cannot be divided into different sub–calculations because the two-fold non-additivity property of VaR. In certain cases of normal distribution returns of a portfolio, an individual can show the “non–additivity” is a “sub–additivity”. Total VaR is constantly equal or less than the sum of partial VaR’s Oldfield, et al (2000).

VaR is in fact receptive to the hedging impact of deterrent positions and the mutual correlation impact of risk drivers. The sub–additivity in VaR of a Gaussian environment embodies the familiar belief that varying lower risks. We are now in a point to appreciate the most recurrent criticisms used against VaR, which in the earlier period gave rise to cruel battles linking opposite factionsAcerbi, et al (2008) .“ VaR constantly come late when the harm is already done”: this adage comes from the fact that for one to approximate market probabilities it is a universal habit to attune potential scenarios on historical market data. For instance, it is apparent that the day...

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