Derives prob ( X + Y < quantile) using Gaussian copula

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Description

If X and Y are position P/Ls, then the VaR is equal to minus quantile. In such cases, we insert the negative of the VaR as the quantile, and the function gives us the value of 1 minus VaR confidence level. In other words, if X and Y are position P/Ls, the quantile is the negative of the VaR, and the output is 1 minus the VaR confidence level.

Usage

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CdfOfSumUsingGaussianCopula(quantile, mu1, mu2, sigma1, sigma2, rho,
  number.steps.in.copula)

Arguments

quantile

Portfolio quantile (or negative of Var, if X, Y are position P/Ls)

mu1

Mean of Profit/Loss on first position

mu2

Mean of Profit/Loss on second position

sigma1

Standard Deviation of Profit/Loss on first position

sigma2

Standard Deviation of Profit/Loss on second position

rho

Correlation between P/Ls on two positions

number.steps.in.copula

The number of steps used in the copula approximation

Value

Probability of X + Y being less than quantile

Author(s)

Dinesh Acharya

References

Dowd, K. Measuring Market Risk, Wiley, 2007.

Dowd, K. and Fackler, P. Estimating VaR with copulas. Financial Engineering News, 2004.

Examples

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# Prob ( X + Y < q ) using Gaussian Copula for X with mean 2.3 and std. .2
   # and Y with mean 4.5 and std. 1.5 with beta 1.2 at 0.9 quantile
   CdfOfSumUsingGaussianCopula(0.9, 2.3, 4.5, 1.2, 1.5, 0.6, 15)

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