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

Description Usage Arguments Value Author(s) References Examples

View source: R/CdfOfSumUsingGumbelCopula.R

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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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)

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 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)

Dowd documentation built on May 30, 2017, 1:30 a.m.