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Hedging 100 short puts using a call delta of 0.25

Question

Calls struck at 2424 on a stock trading at 2121 have delta 0.250.25. You write 100100 puts with the same strike and expiry and want to be delta-neutral. How many shares should you trade? Answer −x-x to sell xx shares.

Short answer

−75-75. Each put has delta 0.25−1=−0.750.25-1=-0.75. Being short 100100 of them gives a position delta of +75+75, which you neutralise by selling 7575 shares.

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