Answer-first summary for fast verification
Answer: −0.4431
## Explanation The delta of a put option on a stock paying a dividend at rate *q* is given by: delta_put = exp(−*q* * *t*) * [N(*d₁*) − 1] Given: - N(*d₁*) = 0.5411 - Dividend yield *q* = 3.5% = 0.035 - Time *t* = 1 year Calculation: delta_put = exp(−0.035 * 1) * (0.5411 − 1) = exp(−0.035) * (−0.4589) = 0.9656 * (−0.4589) = −0.4431 **Why other options are incorrect:** - **A (−0.5517)**: Uses N(*d₂*) instead of N(*d₁*) in the formula - **B (−0.5411)**: Simply −N(*d₁*) without considering the dividend adjustment - **C (−0.4589)**: N(*d₁*) − 1, which would be correct for a non-dividend-paying stock but ignores the dividend adjustment factor exp(−*q* * *t*)
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An options trader is applying the Black-Scholes-Merton option pricing model to estimate the delta of a long 1-year European put option on a dividend-paying stock. Relevant data is provided below:
What is the delta of the put option?
A
−0.5517
B
−0.5411
C
−0.4589
D
−0.4431
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