Question

You wrote(sold short) 1 put option when the put option price was $2, the underlying stock price was $50, and the delta of the put option was -0.65. To achieve delta neutrality, you shorted some shares of the underlying stock. Please fill in the blanks in the following table.

Please show calculations.

Week	Stock price	Put option price per share	Delta	Number of additional shares shorted	Proceeds from short selling additional shares
0	50.00	2	-0.65
1	48.12	3.6	-0.80
2	49.30	2.8	-0.72

Answer 1

When we short a put option, the delta becomes positive as - (negative delta of put) = positive delta.

To acheive delta neutrality, we need to short shares as each shorted share provides a delta of -1 (similarly 0.5 shares shorted will give delta of -0.5).

Initially delta from short put = -(-0.65) = 0.65

Thus we need to short (sell) 0.65 shares

Next, as Put delta changes to -0.8, short position delta becomes 0.8. Thus overall 0.8 shares should be in short position but we already have shorted 0.65 shares. So we need to short sell 0.15 additional shares only to make 0.8

Similarly in week 3, we need to have 0.72 shares short, so we need to buy back 0.08 shares.

The proceeds from short selling additional shares = stock price in that week * additional shares shorted

So the required values for the question are as shown below (calculation formulas shown in next screenshot):

Formulas:

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