Quantitative analysis of social and economic phenomena with mathematical model must follow its assumptions, especially for China's financial industry, because the market still needs to be standardized, the government intervention behavior is more serious, which can not fully meet the strong efficiency and the randomness of market fluctuations. When using the VaR model, it can only be handled approximately normally.
The literal interpretation of VaR is value at risk, that is, the biggest loss that a financial instrument or its combination will face under the fluctuation of asset prices in the future within a certain confidence level and a certain holding period.
Extended data:
VaR basic model
According to Jorion( 1996), VaR can be defined as:
VaR=E(ω)-ω*①
Where E(ω) is the expected value of the portfolio; ω is the final value of the portfolio; ω * is the lowest final value of the portfolio at the confidence level α.
Let ω = ω 0 (1+R) ②.
Where ω0 is the value of the portfolio at the beginning of holding, and r is the return rate of the portfolio within the set holding period (usually one year).
ω*=ω0( 1+R*)③
R * is the lowest rate of return of the portfolio at the confidence level α.
According to the basic properties of mathematical expectation, the formulas ② and ③ are substituted into ①, and there are
VaR = E[ω0( 1+R)]-ω0( 1+R *)
=Eω0+Eω0(R)-ω0-ω0R*
=ω0+ω0E(R)-ω0-ω0R*
=ω0E(R)-ω0R*
=ω0[E(R)-R*]
∴VaR=ω0[E(R)-R*]④
In the above formula, ④ is the VaR value of the portfolio. According to Formula ④, if R * at the confidence level α can be found, the VaR value of the portfolio can be found.
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