Brownian Stock markets

k = 10^6;
f = Interpolation[Accumulate[RandomReal[{-1, 1}, k]]];
frame[t_] := Module[{z, m, \[Mu], \[Zeta]},
  m = k/2;
  z = m 2^-t;
  \[Mu] = f[m];
  \[Zeta] = Sqrt[z];
  Plot[f[x], {x, m - z, m + z},
   PlotRange -> {\[Mu] - \[Zeta], \[Mu] + \[Zeta]}, Axes -> None,
   PlotStyle -> RGBColor[0.8, 0.3, 0.2]]
  ];
Manipulate[frame[t], {t, 0, 10}]