# What time series and length should be used for a second-order derivative?

Let's suppose that

• there is an option on a futures contract,
• the underlying asset for the future is an index, and
• the future is a cash settled contract.

In this case you have a second-order derivative: an option on a future on an index.

I'm going to design an optional combination and then make delta hedging, i.e. buy/sell a certain number of futures contracts.

Edit after Lliane's answer I have a time series (close price of the future), it's length is 2 years (from December, 18, 2014 to December, 15, 2016). The expiration data of the future is Dec, 15, 2016. The traiding volume of future is not uniform and it looks like: I'd like to estimate a distribution of log-returns of the future. For VaR, i should use last 252 days.

Questions

1) What time series should be used in the calculations with this second-order derivative? The futures time series or the index one?

2) What length of time series should be used in the calculations with this second-order derivative?