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Answer: Long about 877 shares.
## Explanation **Given:** - Short 2,000 call options - Current stock price = $19 - Strike price = $20 - Up state: $23.75 - Down state: $15.2 **Delta Calculation using Binomial Model:** Delta = (C_u - C_d) / (S_u - S_d) Where: - C_u = max(S_u - K, 0) = max(23.75 - 20, 0) = 3.75 - C_d = max(S_d - K, 0) = max(15.2 - 20, 0) = 0 - S_u = 23.75 - S_d = 15.2 Delta = (3.75 - 0) / (23.75 - 15.2) = 3.75 / 8.55 ≈ 0.4386 **Hedge Position:** - Short 2,000 calls means negative delta exposure - Delta per option = 0.4386 - Total delta = -2,000 × 0.4386 = -877.2 - To make delta neutral, need to offset with positive delta - Therefore, need to buy 877 shares **Verification:** - Short calls: -877.2 delta - Long 877 shares: +877 delta - Net delta ≈ 0 (delta neutral) The trader should long about 877 shares to make the position delta neutral.
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An option trader is currently holding short positions in 2,000 European call options that will all mature in one month. The current stock price is $19, while the strike price of those call options is $20. The trader is considering the delta hedging strategy based on a simple one-step binomial tree model. In the model setting, one month later, the stock price will be either $23.75 or $15.2. What should the trader do in order to make the position delta neutral?
A
Short about 877 shares.
B
Long about 877 shares.
C
Short about 1,111 shares.
D
Long about 1,111 shares.
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