Answer: Buy 65,000 shares

## Explanation To delta hedge a short call position, the bank needs to buy shares to offset the negative delta from the short calls. **Given information**: - Short position in call options on 100,000 equities - Current stock price (S) = $50 - Strike price (K) = $49 - Time to maturity (T) = 3 months = 0.25 years - Volatility (σ) = 20% - Risk-free rate (r) = 5% **Delta calculation**: For a call option, delta = N(d₁) First calculate d₁: \[ d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_1 = \frac{\ln(50/49) + (0.05 + 0.20^2/2) \times 0.25}{0.20 \times \sqrt{0.25}} \] \[ d_1 = \frac{\ln(1.0204) + (0.05 + 0.02) \times 0.25}{0.20 \times 0.5} \] \[ d_1 = \frac{0.0202 + 0.0175}{0.10} = \frac{0.0377}{0.10} = 0.377 \] Using standard normal distribution: N(0.377) ≈ 0.647 **Total delta hedge**: - Number of options = 100,000 - Delta per option = 0.647 - Total delta = 100,000 × 0.647 = 64,700 Since the bank is short calls (negative delta), they need to buy approximately 65,000 shares to become delta neutral. Therefore, the correct answer is **A: Buy 65,000 shares**.

Author: LeetQuiz Editorial Team