Question

You have just sold a call option on 100 shares of stock. The stock price $74 and its volatility is 60% per annum. The strike price of the option is $86 and it matures in 6 months. The risk-free rate is 4% per annum compounded.

A.) What position should you take in the stock for delta neutrality?

B.) Suppose after you set up the delta-neutral position, the stock price suddenly jumps to 70. Would you buy or sell shares to maintain delta neutrality. Why? Did you gain or lose money or had no gain or loss in your position? Why? You do not need to calculate gain or loss. The explanation is important. Write your answer in the space for the following question.

Answer 1

(a) We Should take LONG POSITION in the stock for delta neutrality because we sold Call option and this trade will have a Negative Delta therefore by taking LONG POSITION in the stock (This trade will give positive delta) we will achieve delta neutrality.

(b) If  the stock price suddenly jumps to 70 we would BUY SHARES because if the share price falls from the delta-neutral position then we have a Net Short position i.e. Negative Delta. Hence to make it Delta Neutral again we have to BUY SHARES.

We will gain because the Call Premium we collected on selling calls is more than than the fall in share Price.