Portfolio neutralisation using options

[Nic88]

How do you neutralise delta and gamma of the following portfolio using a option with delta=0.4, Gamma=1.3 and Vega=0.5?

Long 500 calls with delta=0.5, gamma = 1.2 and vega=1.5
Short 500 calls with delta=0.4, gamma = 0.6 and vega=0.3
Short 2000 puts with delta= -0.8 , gamma = 0.9 and vega=0.7
Short 500 calls with delta=0.7, gamma = 1.3 and vega=1.4

Would your portfolio delta be:
(500x0.5)+(-500x0.4)+(-2000x(-0.8))+(-500x0.7)= 1300?

 

[optstack]

Based on your description, you have assumed a contract multiplier of 1. So using this 1x multiplier, your total portfolio greeks are as follow:

Delta: 1300
Gamma: -2150
Vega: -1500

To neutralize delta and gamma, you could buy the call option to neutralize the gamma and then short stock the neutralize the delta.

To neutralize gamma, you would need to buy the equivalent of 2,150 gamma, which is equal to 1653 units of the call option. (1653 * 1.3 = ~2,150)

Buying the call option would increase your delta of your portfolio by 661 delta, bringing your overall portfolio delta to 1961 (661 + 1300).

To neutralize the delta, you could then sell 1961 shares of stock.


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