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小王爱学习 · 2022年03月24日

累计概率分布图长啥样

NO.PZ2019070101000025

问题如下:

An analyst wants to calculate the value of 1-year European call option and put option using BSM formula. He has collected below information: current stock price is $90, exercise price is $90, continuously compounded risk-free rate is 4%, annual volatility is 20%. What is the value of the call option and put option?

选项:

Call
Put
A.
$10.65
$3.22
B.
$8.93
$5.41
C.
$5.41
$8.93
D.
$3.22
$10.65

解释:

B is correct.

考点:BSM Model

解析:

根据已知条件,可以将BSM模型的参数归纳如下:

S0 =$90; X=$90; r=4% T=1 and σ=20%

d1=ln(9090)+(0.04+0.2×0.22)10.20(1)=0.060.20=0.3

d2=0.3-0.20×1=0.1

从累积概率分布表中查询可以得到

N(d1)=0.6179

N(d2)=0.5398

计算Call option价值:

c=90(0.6179)-90 e 0.04(1) (0.5398)=8.9339

put/call parity, the put’s value is:

p 0 = c 0 s 0 +(X× e R c f ×T )=5.4050

请问老师可以提供一份吗?这个分布大概长什么样子

1 个答案

品职答疑小助手雍 · 2022年03月24日

同学你好,可以直接百度正态分布表,它表达的就是每个分位点对应的累计概率。