A stock is selling at $90. A 3-month call with a strike price of $100 is selling for $3.105 with a delta of 0.329.

Question

How many call contracts are required to perform a hedge on 1,000 shares of this stock? Would they be bought or sold? What happens if the price of the stock falls to $50?

Answer 1

I think what you are asking is how many 33 delta calla would 1000 shares of the underlying stock delta hedge. If One option is on 100 shares then 33 options or one option on 3300 shares will have a delta of 1000 share. This will give you a "static hedge". That is small moves in the share price will bee exactly offset by changes in the value of your short option position. A long stock position will hedge a shot call or a long put position. you would collects 3.105 per share on the 3300 shares or $10,246.5.

If the shares dropped to 50 you would lose $40,000 on the share but would still have the premium of 10,246.5 so your net loss if this all happens at expiration is29,753.5