The price of a non-dividend-paying stock is $49. Consider European call and put

Question

The price of a non-dividend-paying stock is $49. Consider European call and put options underlying the stock with a strike price of $50. The risk-free rate is 6% and the volatility of the stock is 25%. Both options expire in 9 months.

a) If you have written a European call option, what position should you take to make the portfolio delta-neutral?

b) If you have written a European put option, what position should you take to make the portfolio delta-neutral?

c) Find the delta of a long forward contract on one share of the stock.

Explanation / Answer

According to Put-Call Parity,

Cash + Call = Stock + Put

a) If we have written Call, We need to buy Put option and buy stock to make the portfolio Delta Neutral. (Note that we have to create a delta neutral portfolio, Cash investment at risk free rate have zero delta and it does not impact portfolio delta. If we had to hedge it, we would have borrowed present value of strike at Risk-Free Rate)

b) If we have written Put, We need to buy Call option and Sell stock to make the portfolio Delta Neutral.

c) Delta of long forward contract is always = 1

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