Hot answers tagged lognormal
4
I'm not sure I understand, but if you want to compute the variance of $exp(X)$, where $X$ is normally distributed with mean $\mu$ and variance $\sigma^2$, that variance is (from Wikipedia):
$$\left(\exp{(\sigma^2)} - 1\right) \exp{(2\mu + \sigma^2)}$$
3
The distribution of the log of a stock price in n days is a normal
distribution with mean of $\log(current_price)$ and standard deviation of
$volatility*\sqrt(n/365.2425)$ if you're using calendar days, and
assuming no dividends and 0% risk-free interest rate.
Note that the standard deviation is independent of the current_price:
if ...
2
What you have to start with is:
$$dS_t=\mu S_t dt + \sigma S_t dW_t$$
where $W_t$ is a standard brownian motion (SBM).
You want to solve for $S_t$, so how would you proceed?
If you integrate both sides of the equation between 0 and $T$, you get:
$$S_T - S_0= \mu \int_0^T S_t dt + \sigma \int_0^T S_t dW_t$$
Okay and then what? The fact that you have ...
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