Explanation:
Initial delta-neutral position: Williams shorted 2,500 call contracts. Each contract covers 100 shares. Total options shorted = 2,500 * 100 = 250,000. Delta of short options = -250,000 * 0.4563 = -114,075. To be delta neutral, Williams bought 114,075 shares (each share has a delta of 1). Total initial delta = -114,075 + 114,075 = 0.
Delta changes: The new delta per option drops to 0.4168. New delta of short options = -250,000 * 0.4168 = -104,200. Shares still held = 114,075. New total delta = -104,200 + 114,075 = +9,875.
Rebalancing: To make the portfolio delta neutral again (reduce the delta to 0), Williams must offset the excess positive delta of 9,875. Therefore, he needs to sell 9,875 shares.
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Q.59 Robin Williams is considering call options and shares of Xerox Inc. for constructing a portfolio for investment purposes. The 120-day USD 80 call option on Xerox Inc. is trading at USD 2.65. The call option has a delta of 0.4563. Williams sells 2,500 call option contracts (the multiplier is 100) and purchases 114,075 shares of Xerox Inc. The current market price of the stock of Xerox Inc is USD 75. The following month, the prices of both the stock and the call option decrease, and, as a result, the delta decreases to 0.4168. What is the number of shares to be sold/bought by Williams to make the portfolio delta neutral?
A
Sell 9875 shares.
B
Purchase 9875 shares.
C
Sell 99 shares.
D
Purchase 99 shares.