开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

S.J🎈 · 2022年03月11日

u,d,p是怎么求出来的

NO.PZ2020021205000011

问题如下:

A stock price is currently 50. Its volatility is 20% per annum. The risk-free rate is 4% per annum with continuous compounding. Use a two-step tree to determine the value of a six-month European call option on the stock with a strike price of 48.

选项:

解释:

In this case, u = 1.1052, d = 0.9048, and p = 0.5252.

The following two-step tree shows that the value of the

option is 4.511.

  1. 为什么u=e^(10%*1)=0.1052 而不是u=e^(20%*sqrt(1/2))?
  2. p是怎么算出来的?用公式e^(r^change in t)-d/(u-d)里r和change in t分别是多少?为什么?
1 个答案

李坏_品职助教 · 2022年03月11日

嗨,从没放弃的小努力你好:


[公式]


u = exp(σ * √△t),这里的△t表示每一步的年份,本题中是△t=1/4,因为期限是six months, 而且是两步二叉树,所以T = 1/2再除以2 = 1/4.

所以u = exp(20% * √(1/4)) = exp(0.1) = 1.1052


p是价格上涨的概率,p =( exp(4% * 1/4) - 0.9048) / (1.1052-0.9048) = 0.5252


公式的r是无风险利率,因为二叉树模型的理论基础是风险中性概率的世界,折现率统一为risk free rate;change in t就是每一步的年份,这里是1/4


----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

  • 1

    回答
  • 0

    关注
  • 353

    浏览
相关问题

NO.PZ2020021205000011问题如下A stopriis currently 50. Its volatility is 20% per annum. The risk-free rate is 4% per annum with continuous compounng. Use a two-step tree to termine the value of a six-month Europecall option on the stowith a strike priof 48.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 7.5px Helveticcolor: #453e45}span.s1 {color: #655047}span.s2 {color: #303c63}span.s3 {color: #466b}In this case, u = 1.1052, = 0.9048, anp = 0.5252.The following two-step tree shows ththe value of thep.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e45}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}span.s1 {color: #777575}span.s2 {font: 10.0px Helvetica}span.s3 {font: 8.5px Helvetica}span.s4 {color: #6b5547}span.s5 {color: #4b5a6e}option is 4.511.老师您看我哪里算的不对吗?每次算的时候都和答案有差距

2024-06-27 14:07 2 · 回答

NO.PZ2020021205000011问题如下A stopriis currently 50. Its volatility is 20% per annum. The risk-free rate is 4% per annum with continuous compounng. Use a two-step tree to termine the value of a six-month Europecall option on the stowith a strike priof 48.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 7.5px Helveticcolor: #453e45}span.s1 {color: #655047}span.s2 {color: #303c63}span.s3 {color: #466b} In this case, u = 1.1052, = 0.9048, anp = 0.5252.The following two-step tree shows ththe value of thep.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e45}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}span.s1 {color: #777575}span.s2 {font: 10.0px Helvetica}span.s3 {font: 8.5px Helvetica}span.s4 {color: #6b5547}span.s5 {color: #4b5a6e}option is 4.511.请老师帮忙一下,或者我应该去第几节看这个知识点呀

2022-03-28 10:05 1 · 回答

NO.PZ2020021205000011u,p都算出来了,后面不会了,麻烦老师讲解下

2022-03-08 00:16 2 · 回答

这道题年期只有6个月,为什么还是需要两步法求呢?一步算出结果不精确吗

2020-06-30 07:42 1 · 回答