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梦梦 · 2024年07月01日

有两个红框不太明白

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021205000042

问题如下：

What is the vega of a European put option on a stock index when the index level is USD 1,500, the strike price is USD 1,400, the risk-free rate is 5%, the dividend yield is 2%, the volatility is 18%, and the time to maturity is three months. How can this be interpreted?

解释：

The vega is SoT\sqrt T\\N'(d1 )e−qTe^{-qT}\\

In this case, S0 = 1,500, K = 1,400, r = 0.05, q = 0.02, = 0.18, and T = 0.25.

d1=ln⁡(1500/1400)  +  (0.05  −0.02+  0.182/2)  X  0.250.180.25\frac{\ln(1500/1400)\;+\;(0.05\;-0.02+\;0.18^2/2)\;X\;0.25}{0.18\sqrt{0.25}}\\= 0.8949

and vega is

1 500 X 0.25\sqrt{0.25}\\*12πe−0.89492/2×e−0.02×0.25\frac1{\sqrt{2\mathrm\pi}}e^{-0.8949^2/2}\times e^{-0.02\times0.25}\\=199

This means that the value of a long position increases by 199 X 0.01 = 1.99 if volatility increases by 1% (= 0.01) from 18% to 19%. Similarly, it decreases by 1. 99 if the volatility decreases from 18% to 17%.

老师，第一个红框是求导？第二个红框是什么意思？


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2 个答案

品职答疑小助手雍 · 2024年07月02日

没别的意思，这计算过程和delta的那个N（d1）一模一样

梦梦 · 2024年07月06日

好的，谢谢

品职答疑小助手雍 · 2024年07月01日

同学你好，N（d1）就跟BSM公式里面的N（d1）是一样的，是正态分布分位点对应的累计概率。第二个红框是正态分布累计概率计算公式，这个不用掌握，考试时候往往算出来d1之后就会给你几个累计概率值，N（d1）就在里面不需要自己计算。

N（d1）这个知识点是期权定价那章节的核心，建议先看基础班并作为重点学习记牢。

梦梦 · 2024年07月02日

这里的N（d1）我看有个撇，这个没有别的意思是吧？我以为是求导什么的。

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NO.PZ2020021205000042 问题如下 Whis the vega of a Europeput option on a stoinx when the inx level is US1,500, the strike priis US1,400, the risk-free rate is 5%, the vinyielis 2%, the volatility is 18%, anthe time to maturity is three months. How cthis interpretep.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484247}span.s1 {color: #4e2c3f}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #4a5465} p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484246}The vega is SoT\sqrt T\\T​N'( )e−qTe^{-qT}\\e−qTp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4b464c}span.s1 {font: 6.0px Helvetica}In this case, S0 = 1,500, K = 1,400, r = 0.05, q = 0.02, = 0.18, anT = 0.25.=ln⁡(1500/1400)  +  (0.05  −0.02+  0.182/2)  X  0.250.180.25\frac{\ln(1500/1400)\;+\;(0.05\;-0.02+\;0.18^2/2)\;X\;0.25}{0.18\sqrt{0.25}}\\0.180.25​ln(1500/1400)+(0.05−0.02+0.182/2)X0.25​= 0.8949anvega is 1 500 X 0.25\sqrt{0.25}\\0.25​*12πe−0.89492/2×e−0.02×0.25\frac1{\sqrt{2\mathrm\pi}}e^{-0.8949^2/2}\times e^{-0.02\times0.25}\\2π​1​e−0.89492/2×e−0.02×0.25=199This means ththe value of a long position increases 199 X 0.01 = 1.99 if volatility increases 1% (= 0.01) from 18% to 19%. Similarly, it creases 1. 99 if the volatility creases from 18% to 17%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #3f3a41}span.s1 {color: #6b6b6b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4b464c}span.s1 {font: 6.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484449}span.s1 {font: 6.0px Helvetica}span.s2 {font: 8.0px Helvetica}span.s3 {font: 10.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484549}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #544f}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px Helveticcolor: #4532}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473e44}span.s1 {font: 7.0px Helvetica}span.s2 {font: 13.0px Helvetica}span.s3 {color: #42333a}span.s4 {color: #484e6f}span.s5 {color: #6b636b}span.s6 {font: 6.0px Helvetica}span.s7 {color: #7f7b7f}span.s8 {color: #786356}span.s9 {font: 8.0px Helveticcolor: #4532}span.s10 {font: 11.0px Helveticcolor: #4532}span.s11 {color: #4b5a6c}span.s12 {color: #675248}span.s13 {color: #303c63}span.s14 {color: #363536} 老师，VEGA的计算公式是什么?在基础讲义哪页？答案中公式和后面带的数据好像不一致。考纲要求Vega计算吗？谢谢

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vega还需要掌握计算吗？N'（）也不知道怎么算

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