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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


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