15.15 Generate and plot the following processes. Use the time interval [0, 1] and generate the sampled values with frequency Δt = 1/252.

a) A standard Brownian motion started from 0.

b) A Brownian motion with drift μ = 0.01 and volatility σ = 0.3

c) The process St = 100eμt+σBt , with S0 = 100 and parameters as in the previous part.

d) The process Xt = Bt − tB1.

What do you observe about this process? B1 is the value of the Brownian motion at time t = 1.