Delta hedge - maturity

When we are doing the delta hedge, do we need to consider the option’s maturity?

Ex: If we want to hedge the stock over the next 3 months, do we need to choose 3 months’s option? Thanks.

You should choose an option that does not expire before your hedge period ends, to avoid having to roll your entire position (and pay additional transaction costs), and, should the options be in the money, to avoid having them exercised (which will play hob with your hedge).

Thanks. This is question from 2014 Schweser mock vol.1 exam1 Q109

The solution doesn’t care the maturtiy. And the solution is 1 month. (We want to hedge the stock over the next 90 days).

What’s the delta on the options?

Call Option Delta

1m: 0.54

3m: 0.58

6m: 0.61

9m: 0.63

They’re all in the money. The one-month options will likely be exercised at expiration, bollixing up your portfolio.

Or because delta hedge need to continually balance the position anyway, we don’t need to care the maturity?

You do care. In rebalancing, you’re buying or selling a small portion of your options; if they expire, you have to replace all of them. And if they expire in the money, you’ll have to replace the shares of stock that get called (which will be more than the number of shares you hold).

I wouldn’t do it.