Delta Neutral Hedging

CFA Level II Derivatives
#1

When a delta neutral hedge has been established using call options, which of the following statements is most accurate? As the price of the underlying stock:

a. changes, no changes are needed in the number of call options purchased.

b. increases, some option contracts would need to be sold in order to retain the delta neutral position.

c. increases, some option contracts would need to be repurchased in order to retain the delta neutral position.

C is the answer, the explanation is as follows;

The initial delta hedge is established by selling call options (i.e taking a short position in calls). As the stock price increases, the delta of the call option increases as well , requiring fewer (short) option contracts to hedge against the underlying stock price movements. Therefore, some options contracts must be repurchased in order to maintain the hedge. (Purchasing option contracts will decrease the number of call options that we are short)

Question:

Why would the delta of the call option increases as well?

#2

Delta isnt static. As the price increases, so does the rate of delta. Like my other example said, when you are far from the money, detla is going to be close to 0. When you are at the money delta is going to be about .5. When you are deep in the money, delta will be close to 1 (for every dollar stock increass the option increases by 1).

For that reason, your delta hedge will change in small increments overtime… So to keep the delta hedge strategy working, you have to buy or sell more options.