CdfOfSumUsingGumbelCopula {Dowd} | R Documentation |

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

### 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

```
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

```
# 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*version 0.12 Index]