Math Solutions

[All Steps] What is the probability distribution for the stock price S T in 6 month? We know that S T follows a lognormal distribution, and ln S T follows

Question: What is the probability distribution for the stock price S T in 6 month?


We know that S T follows a lognormal distribution, and ln S T follows a normal distribution.


According to Equation (11.2)

\[\ln {{S}_{T}}\tilde{\ }\varphi \left[ \ln S+\left( \mu -\frac{{{\sigma }^{2}}}{2} \right)T,\sigma \sqrt{T} \right]\] ,

where (mean, standard deviation) represents a normal distribution.

Now calculate the mean and the standard deviation for ln S T . (Round your numbers to the nearest 0.001 1 .)

  1. Mean:

  2. Standard Deviation:


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