Brownian bridge simulation

bwn_bridge.py

def gen_bw_bridge(steps, W, n):
    """
    Given a column vector of end values, it will create n brownian bridge
    simulations per value for the amount of steps as defined.
    Can be easily generalized to include random initial values
    and more general start and end times

    steps: integer, how many time intervals there will be 
            between 0 and 1
    W: (sims, 1) nump vector with end values of brownian motion
    n: integer, how many paths per end value to create
    
    MIT License
    """
    assert len(W.shape)==2
    assert W.shape[1]==1
    dt = 1.0 / steps
    sims = W.shape[0]
    W = W.repeat(n)
    W = np.zeros((sims*n, steps+1))
    dW = np.zeros((sims*n, steps))
    s2=1
    s1=0
    x1=0
    x2=W
    for s in range(1, steps+1):
        t = s * dt
        mean = ((s2-t)*x1+(t-s1)*x2)/(s2-s1)
        var = (s2-t)*(t-s1)/(s2-s1)
        W[:, s] = np.random.randn(sims*mult) * sqrt(var)+mean
        s1 = t
        x1 = W[:, s]
    return W