Probability-Stock Price

• Feb 27th 2008, 07:27 PM
taypez
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.

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.
• Feb 27th 2008, 07:39 PM
heathrowjohnny
$\ln S_{T} \sim \phi \left[\ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T, \sigma \sqrt{T} \right]$

So I think $P \left(\text{loss after six months} \right) = \Phi \left(\frac{x - 79.64}{\sigma \sqrt{T}} \right)$ where $\text{mean} = \ln S_{0} + \left(\mu - \frac{\sigma^{2}}{2} \right)T$.
• Feb 27th 2008, 07:58 PM
taypez
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?
• Feb 28th 2008, 04:48 AM
colby2152
Quote:

Originally Posted by taypez
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: $\sigma$