Q-60. Delta hedging the short call option position requires buying shares in an amount equal to the hedge ratio times the 100,000 shares underlying the call position. We can calculate the hedge ratio as N(d₁) from the Black Scholes option pricing model. First we need to compute N(d₁).

d₁ = [ln(50/49) + (0.05 + 0.20²/2) × 0.25] / (0.20 × √0.25) = 0.3770

We know that N(0.3770) has to be between 0.5 and 1.0, which means we need to buy somewhere between 50,000 and 100,000 shares.