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: 1. changes, no changes are needed in the no. of call options purchased 2. increases, some option contracts would need to be repurchased in order to retain the delta neutral position 3. changes, no changes are needed in the no. of call options that are written. 4. increases, some option contracts would need to be sold in order to retain the delta neutral position. Your answer: D was incorrect. The correct answer was B) increases, some option contracts would need to be repurchased in order to retain the delta neutral position. As the stock price increases, the delta of the call option increases as well, requiring fewer option contracts to hedge against the underlying stock price movements. Therefore, some options contracts would need to be repurchased in order to maintain the hedge. In order to maintain delta neutral hedge, don’t we need to write calls instead of buying calls?
Hi, I will try to explain this by a numerical e.g. Number of shares 100,000 (price $60) Delta: 0.5 Options required for D hedge 200,000 (100,000/.5) Now the stock price increases …call value increases…delta increases (say .6) The no of options required for D hedge also changes 166,666(100,000/.6) As less number of options required… repurchase options (200,000-166,666) 33,334. This is not the best example but hope this helps.
delta changes because of gamma
I got it. I was actually confused why we got to repurchase, rather we should sell the options in a dynamic hedging. However, dynamic hedging involves buying shares and writing calls. But if share price increases, and delta increases, we need to write fewer options than what we originally had written - meaning we need to repurchase some. Thanks
very well said MBA&CFA , i was confused by this a little at first too.