A delta-neutral portfolio has a gamma of -1,500. The delta and gamma of a call option...

A delta-neutral portfolio has a gamma of -1,500. The delta and gamma of a call option are 0.4 and 1.5 respectively. a) How many call options is needed to make it gamma-neutral? b) Making the portfolio gamma-neutral causes the portfolio to no longer be delta-neutral. How many shares of the underlying must be sold to keep it delta-neutral?

Expert Solution

A delta-neutral portfolio has a gamma of -1,500.

The delta of a call option is 0.4

The gamma of a call option is 1.5

How many call options is needed to make it gamma-neutral?

Call options is needed to make it gamma-neutral = - (Gamma of delta-neutral portfolio)/ the gamma of a call option

=- (-1,500)/1.5 = 1,500/1.5 = 1000 shares

Making the portfolio gamma-neutral causes the portfolio to no longer be delta-neutral. How many shares of the underlying must be sold to keep it delta-neutral?

Yes it is true that making the portfolio gamma-neutral causes the portfolio to no longer be delta-neutral because the position of option changes.

We should change the position of the underlying asset to maintain delta-neutral.

Number shares of the underlying must be sold to keep it delta-neutral =- (Gamma of delta-neutral portfolio) * the delta of call option

= - (-1,500)* 0.4 = 1,500 * 0.4 = 600 shares

jeff jeffy answered 6 months ago

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