easy · Quantitative Finance stochastic
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?
- 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.
- 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.
- The median price is higher than the expected price, because higher realized volatility always increases the potential for extreme upside price gains.
- 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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