BSM模型中，put的delta是什么？

问题如下：

A European put option has the following characteristics: S₀ =$50;X=$45;r=5%;T=1year;andσ=25%. Which of the following is closest to the value of the put?

Use the BSM formula to solve this question.   N(-0.78644)=0.2158, N(-0.74644)=0.2266, N(-0.49644)=0.3085, N(-0.56644)=0.2855

选项：

A.

$1.88.

B.

$3.28.

C.

$9.07.

D.

$10.39.

解释：

A     S₀ =$50; X=$45; r=5% T=1year and σ=25% ${\text{d}}_1=\frac{\ln(\frac{50}{45})+(0.05+\frac{0.0625}2)1}{0.25(1)}=\frac{0.18661}{0.25}=0.74644$

d₂=0.74644-0.25=0.49644

from the cumulative normal table：

N(-d₁)=0.2266

N(-d₂)=0.3085*

$p=45e^{-0.05(1)}(0.3085)-50(0.2266)=1.88$

(*note rounding)