Question

The value of certain fund (which is essentially a long position in a certain index) is basically 1,000,000x INDEX. Now the manager contemplates adding some options on the index to make his fund delta-neutral. There are two options available with the following characteristics: Option 1 with price currently 10.30 has a delta of 0.6151 and Option 2 with current price 6.06 and delta of 0.4365. Which option should he use? There are any other ways to solve this problem? Include formulas . Be specific, explain every step. What will affect the decision if delta goes up or down? How this action will affect delta neutral? What will happen if the price goes up or down of both options? What if the fund is holding for short position? There are any other characteristics that will affect the decision? Be sure to explain every detail.

Answer 1

Delta is the change in the price of the option in relation to the change in the price of the underlying.

For a delta neutral position the total of all deltas should be 0.

The long position on the index has a delta of 1. To be delta neutral he should short both the options

Then the total delta will be 1 – 0.6151 – 0.4365 = - 0.0516 which is close to 0.

If the delta goes up or down he has to add or remove options till it is delta neutral again.

If the fund is holding for short daysposition then he has to buy the call options.

The no of days to expiry and implied volatility will also affect the decision.