def test_MartingalePropertyTimeDependentParameters(self):
d = 2
times = np.array([2.0, 4.0])
sigmaT = np.zeros([2, 2, 2])
sigmaT[0, :, :] = np.array([[0.10, 0.15], [0.20, 0.25]])
sigmaT[1, :, :] = np.array([[0.15, 0.20], [0.25, 0.30]])
chi = np.array([0.1, 0.2])
#
model0 = MarkovFutureModel(None, d, times, sigmaT, chi)
#
times = np.linspace(0.0, 5.0, 6)
nPaths = 2**10
seed = 314159265359
sim = McSimulation(model0,
times,
nPaths,
seed,
False,
showProgress=False)
dT = np.linspace(0.0, 5.0, 3)
for k, t_ in enumerate(times):
for dT_ in dT:
F = np.array([
model0.futurePrice(t_, t_ + dT_, X, None)
for X in sim.X[:, k, :]
])
#print(np.abs(np.mean(F) - 1.0))
self.assertLess(np.abs(np.mean(F) - 1.0), 0.07)
def test_CompareWithMarkovModel(self):
kappa = 1.35
sigma_0 = 0.50
sigma_infty = 0.17
rho_infty = 0.50
model0 = AndersenFutureModel(None,kappa,sigma_0,sigma_infty,rho_infty)
#
def sigmaT(sigma_0, sigma_infty, rho_infty):
h1 = -sigma_infty + rho_infty * sigma_0
h2 = sigma_0 * np.sqrt(1.0 - rho_infty**2)
hi = sigma_infty
return np.array([ [h1, h2], [hi, 0.0] ])
#
def chi(kappa):
return np.array([ kappa, 0.0 ])
#
sigmaT_ = sigmaT(sigma_0,sigma_infty,rho_infty)
chi_ = chi(kappa)
#
d = 2
times = np.array([0.0])
model1 = MarkovFutureModel(None,d,times,np.array([ sigmaT_ ]),chi_)
#
times = np.linspace(0.0, 5.0, 3)
nPaths = 2**3
seed = 14159265359
#
sim0 = McSimulation(model0,times,nPaths,seed,False,showProgress=False)
sim1 = McSimulation(model1,times,nPaths,seed,False,showProgress=False)
#
for idx in range(1,times.shape[0]):
t = times[idx]
for dT in [ 0.0, 1.0, 2.0, 5.0, 10.0]:
T = t + dT
F0 = np.array([ model0.futurePrice(t,T,X,None) for X in sim0.X[:,idx,:] ])
F1 = np.array([ model1.futurePrice(t,T,X,None) for X in sim1.X[:,idx,:] ])
# print(F0-F1)
self.assertLess(np.max(np.abs(F0-F1)),3.0e-16)