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Answer: buy 65,000 shares
A is correct. 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. The only answer that fits is A, buy 65,000 shares. If you did have access to a probability table, you could determine that N(0.3770) = 0.6469, which means we need to buy exactly 64,690 shares to delta hedge the position.
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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.
A
buy 65,000 shares
B
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