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.