# CdfOfSumUsingGaussianCopula: Derives prob ( X + Y < quantile) using Gaussian copula In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

## 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

 ```1 2``` ```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

Dinesh Acharya

## References

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

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

## Examples

 ```1 2 3``` ```# 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) ```

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