def test_AuxilliaryStateVsQuasiGaussian(self):
curve = YieldCurve(0.03)
d = 3
times = np.array([1.0, 2.0, 5.0, 10.0])
sigma = np.array([[0.0060, 0.0070, 0.0080, 0.0100],
[0.0030, 0.0035, 0.0040, 0.0050],
[0.0025, 0.0025, 0.0025, 0.0025]])
slope = np.zeros([3, 4])
curve = np.zeros([3, 4])
delta = np.array([1.0, 5.0, 20.0])
chi = np.array([0.01, 0.05, 0.15])
Gamma = np.array([[1.0, 0.8, 0.6], [0.8, 1.0, 0.8], [0.6, 0.8, 1.0]])
qGmodel = QuasiGaussianModel(curve, d, times, sigma, slope, curve,
delta, chi, Gamma)
X0 = qGmodel.initialValues()
#T = np.linspace(-1.0, 11.0, 121)
#vols = np.array([ qGmodel.sigma_xT(t,X0) for t in T ])
#plt.plot(T,vols[:,0,0],label='sigma[0,0]')
vols = np.array([qGmodel.sigma_xT(t, X0) for t in times])
#plt.plot(times,vols[:,0,0],'*',label='sigma[0,0]')
#plt.show()
#
mVmodel = MarkovFutureModel(None, d, times, vols, chi)
# we need to evolve the Quasi Gaussian model to obtain y(t)
times = np.linspace(0.0, 11.0, 111)
sim = McSimulation(qGmodel, times, 1, 1, showProgress=False)
Y0 = sim.X[0, :, d:d + d * d]
Y0.shape = [111, 3, 3]
Y1 = np.array([mVmodel.y(t) for t in times])
# print(np.max(np.abs(Y1[1:]/Y0[1:] - 1.0)))
self.assertLess(np.max(np.abs(Y1[1:] / Y0[1:] - 1.0)), 6.2e-14)
def test_ZeroMeanReversion(self):
d = 2
times = np.array([0.0])
sigmaT = np.zeros([1, 2, 2])
sigmaT[0, :, :] = np.array([[0.10, 0.15], [0.20, 0.25]]).T
dt = 2.0
dW = np.ones(2)
for chi1_ in [
1.0e-4, 1.0e-5, 1.0e-6, 1.0e-7, 1.0e-8, 1.0e-10, 1.0e-12,
1.0e-14, 0.0
]:
chi0_ = 0.1
model0 = MarkovFutureModel(None, d, times, sigmaT,
np.array([chi0_, chi1_]))
model1 = MarkovFutureModel(None, d, times, sigmaT,
np.array([chi0_, 0.1 * chi1_]))
#
X0 = model0.initialValues()
X1_0 = model0.initialValues()
X1_1 = model0.initialValues()
#
model0.evolve(0.0, X0, dt, dW, X1_0)
model1.evolve(0.0, X0, dt, dW, X1_1)
#
# print(np.max(np.abs(X1_0 - X1_1)))
self.assertLessEqual(np.max(np.abs(X1_0 - X1_1)), chi1_)
def test_SigmaFunction(self):
d = 2
times = np.array([1.0, 3.0])
sigmaT = np.zeros([2, 2, 2])
sigmaT[0, :, :] = np.array([[0.50, 0.60], [0.70, 0.80]])
sigmaT[1, :, :] = np.array([[0.55, 0.65], [0.75, 0.85]])
chi = np.array([0.1, 0.2])
#
model = MarkovFutureModel(None, d, times, sigmaT, chi)
#
T = np.linspace(-1.0, 5.0, 13)
vols = np.array([model.sigmaT(t) for t in T])
# plt.plot(T,vols[:,0,0],label='sigma[0,0]')
# plt.plot(T,vols[:,0,1],label='sigma[0,1]')
# plt.plot(T,vols[:,1,0],label='sigma[1,0]')
# plt.plot(T,vols[:,1,1],label='sigma[1,1]')
# plt.legend()
# plt.show()
refVols = np.array([[[0.5, 0.6], [0.7, 0.8]], [[0.5, 0.6], [0.7, 0.8]],
[[0.5, 0.6], [0.7, 0.8]], [[0.5, 0.6], [0.7, 0.8]],
[[0.5, 0.6], [0.7, 0.8]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]],
[[0.55, 0.65], [0.75, 0.85]]])
self.assertEqual(np.max(np.abs(vols - refVols)), 0.0)
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_KnownSimulationValues(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]]).T
sigmaT[1, :, :] = np.array([[0.15, 0.20], [0.25, 0.30]]).T
chi = np.array([0.1, 0.2])
#
model0 = MarkovFutureModel(None, d, times, sigmaT, chi)
#
times = np.linspace(0.0, 5.0, 6)
nPaths = 2**3
seed = 314159265359
sim = McSimulation(model0,
times,
nPaths,
seed,
False,
showProgress=False)
# np.set_printoptions(precision=16)
# print(sim.X[:,-1,:])
Xref = np.array([[-0.6000110699011598, -0.6431768273428073],
[0.138146279288649, 0.1270588210285978],
[-0.2615455421299724, -0.3054110432018231],
[-1.1042559026028758, -1.0151899131194109],
[-0.934746072227638, -1.1542393979975838],
[-0.0771484387711384, -0.1328561062878627],
[-0.5411246272833143, -0.4660671538747663],
[0.6805897799894314, 0.7389950985079005]])
#print(np.max(np.abs(sim.X[:,-1,:]-Xref)))
self.assertLess(np.max(np.abs(sim.X[:, -1, :] - Xref)), 1.2e-16)
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)
def test_AuxilliaryState(self):
d = 2
times = np.array([0.0])
sigmaT = np.zeros([1, 2, 2])
sigmaT[0, :, :] = np.array([[0.50, 0.60], [0.70, 0.80]])
chi = np.array([0.1, 0.2])
#
model0 = MarkovFutureModel(None, d, times, sigmaT, chi)
self.assertEqual(np.max(np.abs(model0._y - np.zeros([1, 2, 2]))), 0.0)
#
times = np.array([1.0, 3.0])
sigmaT = np.zeros([2, 2, 2])
sigmaT[0, :, :] = np.array([[0.50, 0.60], [0.70, 0.80]])
sigmaT[1, :, :] = np.array([[0.50, 0.60], [0.70, 0.80]])
#
model1 = MarkovFutureModel(None, d, times, sigmaT, chi)
T = np.linspace(0.0, 5.0, 6)
y0 = np.array([model0.y(t) for t in T])
y1 = np.array([model1.y(t) for t in T])
self.assertLess(np.max(np.abs(y0 - y1)), 1.0e-15)