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)