Explanation:
First, calculate the delta of the short call position. The investor sold 100 contracts, each on 100 shares.
Total options sold = $100 \times 100 = 10,000-10,000 \times 0.60 = -6,000$.
To make the position delta-neutral initially, the investor must buy 6,000 shares of the underlying stock (providing a delta of +6,000).
Later, the stock price falls, and the option's delta decreases by 10%.
New option delta = $0.60 \times (1 - 0.10) = 0.54-10,000 \times 0.54 = -5,4006`,000 - 5,400 = +600$.
To rebalance the portfolio to delta-neutral, the investor must decrease the delta by 600, which requires selling 600 shares of the stock.
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Q.61 A non-dividend-paying stock has a current price of USD 100. You have just sold 100 1-year European call options contracts each on 100 shares of this stock at a price of USD 102 per share. To hedge the risk that comes with selling the options, you want to put in place a robust and dynamic delta-hedging scheme. Each of the options has a delta of 0.60. If the stock price falls to USD 95 per share, you believe the delta would reduce by 10%. Identify what action you should take now (immediately after writing the contract) to make your overall position delta neutral. After writing the contract, if the stock price falls to USD 95, what action should you take at that time so as to rebalance your hedged position?
A
Now: buy 60 shares of stock; Later: buy 6 shares of stock
B
Now: sell 6,000 shares of stock; Later: buy 600 shares of stock
C
Now: buy 6,000 shares of stock; Later: sell 600 shares of stock
D
Now: sell 6,000 shares of stock; Later: sell 600 shares of stock
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