Suppose you have three positions in the following assets in euros: long on 10.000 calls (maturity T = 3 months, strike= 0.55, Delta (1 call) =0.533), short on 210000 calls (maturity T = 3 months, strike= 0.56, Delta (1 call) =0.468), short on 20000 puts (maturity T = 3 months, strike= 0.56, Delta (1 put) =-0.8944). You can make your portfolio delta-neutral (a) with a long position on 75062 euros (b) with a short position on 75062 euros; (c) with a long position on 75062 calls; (d) with a short position on 75062 puts.

I tried to compute the portfolio's Delta by summing the Delta of the derivatives an multiplying them for the number of options. Then I tried to dived the portfolio's delta by the derivatives' delta one by one to find out how many calls or puts i had to sell/buy to make the portfolio delta neutral. Then I tried to convert the results in euro but none of my attempets brough me somewhere near the number 75062. Can you please help me?

  • $\begingroup$ As far as I know, you can calculate your position delta, as you have said in the first sentence, by summing the deltas and multiplying them against each of their position: $\Delta_\Pi=10000\cdot 0.533-210000\cdot 0.468-20000\cdot (-0.8944)=-75062EUR$. This implies that a 1EUR increase in the underlying will give you a loss of -75062 EUR. We know that the delta of the underlying is 1, then we can add a position of 75062EUR of stock to our portfolio, in order to make it delta-neutral in the moment. I believe this should be the essence of the question. $\endgroup$ – Pleb Jan 27 at 9:16

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