CFA Level I · CFA Level I Exam · Pricing and Valuation of Options
A dealer is short 1,000 call options on a stock, each on one share, and is delta hedged with the call delta at 0.50 and gamma at 0.04 per share. The stock then rises by USD 2 quickly before the dealer rebalances. Using delta plus gamma, the new delta of each call is closest to:
The new delta is about 0.58. Gamma measures the change in delta per USD 1 move in the underlying, so a USD 2 rise adds 0.04 x 2 = 0.08 to the original delta of 0.50, giving 0.58.
- A0.54
- B0.58Correct
- C0.62
Explanation
New delta = 0.50 + 0.04 x 2 = 0.58. The option delta rises by gamma times the price change. 0.54 uses only a USD 1 move, and 0.62 would need a USD 3 move. The short position is now under-hedged since the dealer's short calls have more negative delta, requiring more shares to be bought.
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