A non-dividend-paying stock has a current price of $100 per share. You have just sold a six-month European call option contract on 100 shares of this stock at a strike price of $101 per share. You want to implement a dynamic delta hedging scheme to hedge the risk of having sold the option. The option has a delta of 0.50. You believe that delta would fall to 0.44 if the stock price falls to $99 per share. Identify what action you should take now (i.e., when you have just written the option contract) to make your position delta neutral. After the option is written, if the stock price falls to $99 per share, identify what action should be taken at that time, i.e., later, to rebalance your delta-hedged position.
A. Now: buy 50 shares of stock; later: buy 6 shares of stock.
B. Now: buy 50 shares of stock; later: sell 6 shares of stock.
C. Now: sell 50 shares of stock; later: buy 6 shares of stock.
D. Now: sell 50 shares of stock; later: sell 6 shares of stock.