Choosing Futures Data for Hedging an Option on an Index Future

Summary

The document asks whether to estimate log-return risk for an option on a cash-settled index future using futures prices or the underlying index, and how much history to use. The response focuses on the hedge instrument: because the option exposure is to the future, hedging with futures data aligns the risk estimate with the position and avoids basis risk that can arise from using the index instead.

The question mentions a two-year futures closing-price series, an expiring contract, uneven trading volume, and a proposed 252-day window for Value at Risk. The answer does not assess whether that history length or VaR window is suitable, nor does it discuss rolling between futures contracts, liquidity effects, or model assumptions. Its useful guidance is limited to matching the series to the instrument being hedged; the choice of estimation period remains unresolved.

Key ideas

• For an option on a futures contract, the direct hedge exposure is to the future.
• Using futures returns for the hedge risk estimate can avoid basis risk from using the underlying index.
• The response does not specify how much historical data to use.
• It does not address contract rolls, uneven volume, or VaR model choices.

Tags

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


# 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?

## Answer by Lliane (score 3)

https://quant.stackexchange.com/a/31184

Your exposure is on the future contract, not the underlying asset so I would hedge based on the future, or else you'll have basis risk.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.