为啥不是（1-N(d1)）啊？另外，求delta的公式是怎么来的啊？

问题如下：

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(d₁): 0.5411

· N(d₂): 0.4287

What is the delta of the put option?

选项：

−0.5517

−0.5411

−0.4589

−0.4431

解释：

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(d₁ ) – 1]. Given that N(d₁) = 0.5411,

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(d₂) is used instead of N(d₁) in the formula above.

B is incorrect. −0.5411 is −N(d₁).

C is incorrect. −0.4589 is N(d₁) – 1, which would be the delta of the option if the stock were dividend-free.