Out of the many ways that make it possible to extract a single number out of a density curve, the one chosen in the context of VaR is the following:įor a given probability C referred as confidence level (typically C equals. Its justification lies on the fact that human brains and automation systems come better in terms with single numbers than the infinity of numbers implied by a curve. This requirement may be seen as unnecessarily restrictive, given the fact that a density curve conveys much more information about the riskiness of the referenced asset than any single number in the world. Since we have so far described VaR as an amount, it turns out that a single number must be somehow associated with the density curve. The exact shape of that function depends on both the type of the involved asset and our assumptions about the stochastic evolution of the particular market prices that affect the asset value.įor illustration purposes, a possible probability density function for the asset value at horizon could look like that: Therefore, all boils down to establishing the probability distribution – or equivalently the probability density – function of the asset values V i that may be realized at horizon. Under the assumption that we ignore extreme losses L i that are deemed too unlikely to occur, the statement worst possible future loss becomes tenable. If a value V i, were realized at horizon, it would lead to a respective realized asset loss L i = V 0 – V i, where V 0 is the current asset value. This is indeed so, since there exist infinite possible values V i that the underlying asset may assume at horizon. Second, the two words worst possible imply the existence of several candidate losses. It is conventionally set to either one day or two weeks from today, with the respecting VaR being the one-day or two-week VaR. This time instant is commonly called the VaR horizon. In order to be able to compute the VaR, the underlined phrase worst possible future loss deserves a precise, technical definition.įirst, the word future is construed to refer to some fixed time instant that has not yet occurred. Using imprecise language, the Value at Risk – abbreviated as VaR – of a particular asset is just an amount, for example $1M, which represents the worst possible future loss sustained by that asset.
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