Explanation:
The trader sold 100 option contracts, each covering 100 shares, resulting in an exposure of -10,000 options. Since the delta is 0.60, the overall position delta is -10,000 × 0.60 = -6,000. To make the position delta-neutral, the trader needs to purchase +6,000 shares of the underlying stock. If the stock price falls and the delta reduces by 10%, the new delta is 0.60 × (1 - 0.10) = 0.54. The new position delta is -10,000 × 0.54 = -5,400. To rebalance to delta-neutral, the trader must hold 5,400 shares. Since 6,000 shares were already purchased, the trader must sell 600 shares (6,000 - 5,400 = 600) to adjust the hedge.
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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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