老师，这题可以用无套利方法算吗？我算出来的p0是0.546，不知道是哪里算错了

问题如下：

A manager wants to price a put option by one-period binomial tree. The relative information is as follows:

• The current stock price is $30, exercise price of put option is $30
• The up factor is 1.12, and the down factor is 0.92
• The risk-free rate is 5%.

The value of this put option is:

选项：

A.

0.6

B.

0.84

C.

0.8

解释：

C is correct.

考点：一期二叉树对股票期权定价

解析：

向上的概率π_u =[(1+rf)-d ]/(u-d) = [(1+5%)-0.92] / (1.12-0.92)=0.65

向下的概率πd=1-0.65=0.35

p⁺=max(0, X-S⁺)=max(0,30-30×1.12)=0

p^-=max(0, X-S^-)=max(0,30-30×0.92)=2.4

$P_0=\frac{0\times0.65+2.4\times0.35}{1+5\%}=0.8$