easy · Quantitative Finance

Under the Geometric Brownian Motion model with drift μ = 0.12 and volatility σ = 0.30, which of the following is true regarding the expected price E[S_1] and the median price S_median of a stock after one year if S_0 = 100?

1. The median price is calculated using only the volatility σ and the current spot price level, but it entirely ignores the drift term μ altogether.
2. The median price is lower than the expected price due to 'volatility drag' represented by the -(1)/(2)σ^2 term in the log-drift.
3. The median price is higher than the expected price, because higher realized volatility always increases the potential for extreme upside price gains.
4. The expected price and median price here are equal, since this model assumes the stock price follows a symmetric normal distribution.

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