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Math Help - Probability-Stock Price

  1. #1
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    Probability-Stock Price

    The price of a stock is governed by a log normal distribution with the expected growth rate μ=.12, volatility, σ=.2. The initial price is $75.

    I have already calcuated:

    E(stock price after 6 months) = 79.64

    V = 128.12

    σ = 11.32

    How do I show that the probability of a loss after 6 months is 0.3372?

    Thanks.
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  2. #2
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     \ln S_{T} \sim \phi \left[\ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T, \sigma \sqrt{T} \right]


    So I think  P \left(\text{loss after six months} \right) = \Phi \left(\frac{x - 79.64}{\sigma \sqrt{T}} \right) where  \text{mean} = \ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T .
    Last edited by heathrowjohnny; February 27th 2008 at 08:51 PM.
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  3. #3
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    so, is x the mean? Just to clarify, is the μ and σ that I use to calculate the mean the ones that I calculated and not the ones that are given?
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by taypez View Post
    so, is x the mean? Just to clarify, is the μ and σ that I use to calculate the mean the ones that I calculated and not the ones that are given?
    Mean: \mu
    Standard deviation: \sigma
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