VA's with Gaurantees

do we need an extra 0.5 yr zero rate, in order to back out other zero rates from swap?

Yes, but just assume that the 6 month rate is the same as the one year rate.

In class, you give us an example of swap rate and zero-coupon rate. For the fixed side, you divide the 2-year swap rate by 2 and discounted. What is the assumption of the swap rates? For a point such as 2.5 year, how do we deal with it? Thanks.

The swap rate is actually a six month rate so you do indeed divide it by 2.

For years like 2.5, you need some kind of interpolation assumption. I it OK to just use linear interpolation.

if im using 1000 scenarios to get one averaged price, when workin out the confidence interval, should i do it directly from this 1000 scenarios, or should i run, e.g. 1000*1000 scenarios, and get the interval from 1000 'averaged prices'? hope i made myself clear..

Thanks a lot~

You are looking for a 95% confidence interval for the estimator. So yes, you would want to "estimate" using 1000 scens, and then repeat it again and again and again in order to get an empirical distribution of the estimator.