How many shares to hedge 200 short call contracts

Question

You sell 200 call contracts on a stock. Each contract covers 100 shares, and the call's delta is 0.35. The stock is at \80. How many shares must you trade, and in which direction, to be delta-neutral? What happens to that hedge if the stock rallies?

Accepted Answer

Start with the position's delta in share-equivalents. A long call has delta +0.35; you are short 200 contracts, so your option delta is \Delta{	ext{position}} = -0.35 	imes 200 	imes 100 = -7{,}000 	ext{ shares.} You are effectively short 7{,}000 shares of exposure: if the stock rises \1 you lose about \7{,}000 on the options. To flatten, take the opposite share position: buy 7{,}000 shares. Now the +7{,}000 from stock cancels the -7{,}000 from the short calls. The catch, gamma. A short call is short gamma. If the stock rallies, the call's delta climbs (say from 0.35 toward 0.55), so your…

How many shares to hedge 200 short call contracts

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