Exercise

# Estimating VaR and ES for option portfolio

Now you are ready to estimate VaR and ES for the investor in the European call option using the historically simulated losses and gains in `hslosses`

.

Once again, you will do this by two methods. First, you will apply a non-parametric method using a sample quantile to estimate VaR and calculate the average of values exceeding the same quantile to estimate ES.

Then, you will compare these estimates with the values obtained when you assume that the `hslosses`

have a normal distribution. Like in the previous exercise, this is a bad assumption and you should compare the two sets of estimates to see which are more conservative.

Instructions

**100 XP**

- Estimate the 99.5% sample percentile of the distribution of
`hslosses`

using`quantile()`

. - Estimate the 99.5% ES by computing the mean of the
`hslosses`

that are at least as large as the VaR estimate (this has been done for you). - Use the appropriate functions to estimate the mean and standard deviation of
`hslosses`

and assign to`mu`

and`sigma`

, respectively. - Use
`qnorm()`

with the calculated mean and standard deviation to compute the 99.5% quantile of a normal distribution. - Use
`ESnorm()`

with the calculated mean and standard deviation to compute the 99.5% ES of a normal distribution.