Calculate general Brownian motion and geometric Brownian motion properties: increment distribution, expected price, drift and diffusion effects
A general Brownian motion process is defined as:
X(t) = μt + σB(t)
where μ is the drift coefficient and σ is the diffusion coefficient.
A geometric Brownian motion process is defined as:
S(t) = S₀e^(μt + σB(t))
where S₀ is the initial price, μ is the expected return rate, and σ is the volatility.