You hold a portfolio consisting of long 60 shares and short 1 call option. The option’s underlying is 100 shares. The po

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You hold a portfolio consisting of long 60 shares and short 1
call option. The option’s underlying is 100 shares. The portfolio
is delta neutral with Gamma of -150 and Vega of -120. Construct a
delta-gamma-vega-neutral portfolio when the following options are
available: Call option 1 with Delta=0.5, Gamma=2, Vega=1.5 Call
option 2 with Delta=0.4, Gamma=0.8, Vega=1 Show the steps and
number of positions regarding in each asset in the required
Delta-gammavega-neutral portfolio.
part answer below but how do they work out the values of N1 and
N2?
Step 1, estimate number of options C1 and
C2
-150 + 2×N1 + 0.8×N2 = 0 (make the portfolio Gamma-neutral)
-120 + 1.5×N1+1×N2 = 0 (make the portfolio Vega-neutral)
N1 = 67.5 we need 67.5/100=0.675 C1
N2=18.75 we need 18.75/100=0.1875 C2