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P1.T4.404. Neutralizing option position Greeks

Nicole Seaman

Chief Admin Officer
Staff member
AIM: Explain how to implement and maintain a gamma neutral position


404.1. A European call option has a (percentage) delta of 0.580. A trader creates a straddle by purchasing 1,000 of the call options and 1,000 put options with identical strike and maturity. However, the trader wants to neutralize delta. Which of the following trades, when added to the straddle, will neutralize the total position's delta?

a. Short 1,380 of the call options
b. Short 160 of the underlying shares
c. Long 720 of the put options
d. No additional trade required as the straddle is already delta neutral

404.2. Robert the Trader has already written 1,000 call options with (percentage) delta of 0.670 and gamma of 0.090 such that his position delta is -670.0 and his position gamma is -90.0. He can buy or sell another call option on the stock; this additional call option has (percentage) delta of 0.560 and gamma of 0.150. Which trade will neutralize delta and gamma?

a. Buy 600 call options and buy 334 of the underlying shares
b. Buy 400 call options and sell 215 of the underlying shares
c. Sell 300 call options and buy 180 of the underlying shares
d. Sell 260 call options and sell 155 of the underlying shares

404.3. A portfolio has the following position Greeks: delta = -300, gamma = -150, and vega = -3,000. A trader wants to neutralize all three Greeks and, in addition to the underlying shares, can use the following two options:
  • Call option with the following percentage Greeks: delta = 0.60, gamma = 0.20, and vega = 10.0
  • Put option with the following percentage Greeks: delta = -0.40, gamma = 0.30, and vega = 20.0
Along with the underling shares, which set of trades will make the total position delta-gamma-vega neutral? (hint: first make the portfolio gamma-vega neutral, then use shares to neutralize delta)

a. Short 800 of the calls; long 150 of the puts, and short 500 of the underlying shares
b. Short 1,500 of the calls; short 680 of the puts, and long 770 of the underlying shares
c. Long 2,100 of the calls; short 900 of the puts; and short 1,320 of the underlying shares
d. Long 3,000 of the calls; short 1,750 of the puts; and long 540 of the underlying shares

Answers here: