Financial Risk Manager Part 1

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Explanation:

D is correct. The delta of a put option on a stock paying a dividend at rate $q$ is given by $\exp(-q * t) * [N(d_1) - 1]$ . Given that $N(d_1) = 0.5411$ :

$\text{delta} = \exp(-0.035 * 1) * (0.5411 - 1)$

$= \exp(-0.035 * 1) * -0.4589 = -0.4431$

A is incorrect. $-0.5517$ is the result if $N(d_2)$ is used instead of $N(d_1)$ in the formula above.

B is incorrect. $-0.5411$ is $-N(d_1)$ .

C is incorrect. $-0.4589$ is $N(d_1) - 1$ , which would be the delta of the option if the stock were dividend-free.

Learning Objective: Compute the delta of an option.

Explanation:

D is correct. The delta of a put option on a stock paying a dividend at rate $q$ is given by $\exp(-q * t) * [N(d_1) - 1]$ . Given that $N(d_1) = 0.5411$ :

$\text{delta} = \exp(-0.035 * 1) * (0.5411 - 1)$

$= \exp(-0.035 * 1) * -0.4589 = -0.4431$

A is incorrect. $-0.5517$ is the result if $N(d_2)$ is used instead of $N(d_1)$ in the formula above.

B is incorrect. $-0.5411$ is $-N(d_1)$ .

C is incorrect. $-0.4589$ is $N(d_1) - 1$ , which would be the delta of the option if the stock were dividend-free.

Learning Objective: Compute the delta of an option.

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Question 11. 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:

Annual continuously compounded risk-free rate of interest: 2.0%

Annual dividend yield on the stock: 3.5%

$N(d_1)$ : 0.5411

$N(d_2)$ : 0.4287

What is the delta of the put option?

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UAnonymous

Last updated: July 10, 2026 at 05:44

$-0.5517$

$-0.5411$

$-0.4589$

$-0.4431$