/Heston-Model-

Heston-Model-

def function (S0, mu, v0, rho, kappa, theta, etha, T, dt) :

# Generate a Montcarlo simulation for the Heston Model

# Generate random Brownian Motion

Mu = np.array([0, 0])
COV = np.matrix([[1, rho], [rho, 1]])
W = np.random.multivariate_normal(MU, COV, T)
    W_S = W[:,0]
    W_v = W[:,1]

    # Generate paths
vt    = np.zeros(T)
vt[0] = v0
St    = np.zeros(T)
St[0] = S0
for t in range(1,T):
    vt[t] = np.abs(vt[t-1] + kappa*(theta-(vt[t-1]))*dt + etha*np.sqrt((vt[t-1]))*W_v[t]*np.sqrt(dt))
    St[t] = St[t-1]*np.exp((mu - 0.5*vt[t-1])*dt + np.sqrt(vt[t-1]*dt)*W_S[t])

return St, vt