CdfOfSumUsingGumbelCopula function

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

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.

CdfOfSumUsingGumbelCopula(quantile, mu1, mu2, sigma1, sigma2, beta)

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
• beta: Gumber copula parameter (greater than 1)

Returns

Probability of X + Y being less than quantile

Examples

# Prob ( X + Y < q ) using Gumbel 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
   CdfOfSumUsingGumbelCopula(0.9, 2.3, 4.5, 1.2, 1.5, 1.2)

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.