Answer: Buy 65,000 shares

## Explanation To delta hedge a short call position, the bank needs to buy shares to offset the negative delta exposure. **Key Information:** - Number of options: 100,000 - Stock price (S) = $50 - Strike price (K) = $49 - Time to maturity (T) = 0.25 years (3 months) - Volatility (σ) = 20% - Risk-free rate (r) = 5% **Delta Calculation:** The delta of a call option is given by N(d₁), where: d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) Let's calculate: d₁ = [ln(50/49) + (0.05 + 0.20²/2)×0.25] / (0.20×√0.25) d₁ = [ln(1.02041) + (0.05 + 0.02)×0.25] / (0.20×0.5) d₁ = [0.02020 + 0.0175] / 0.10 d₁ = 0.0377 / 0.10 = 0.377 Delta = N(0.377) ≈ 0.647 **Hedge Position:** - Bank sold 100,000 call options - Each option has delta of approximately 0.647 - Total delta exposure = -100,000 × 0.647 = -64,700 - To hedge, need to buy 64,700 shares - Rounded to nearest thousand: 65,000 shares Therefore, the bank should buy 65,000 shares to delta hedge the short call position.

Author: LeetQuiz .