def test_create(self):
vec = self.vec
last = len(vec)-1
idx = 1
d = np.hstack((np.nan, np.diff(vec)))
deltas = d
sch0 = 'center'
axis = 1
for sch1 in ['center', 'up', 'down']:
for dv in [1,2]:
oldX1 = utils.nonuniform_complete_coefficients(deltas, up_or_down=sch1, flip_idx=idx)[dv-1]
X1 = FD.BO.for_vector(vec, scheme=sch1, derivative=dv, order=2, axis=axis)
high, low = 1,-1
if (sch0 == 'up' and idx > 1) or (sch1 == 'up' and idx < last-1):
high = 2
if (sch0 == 'down' and idx > 2) or (sch1 == 'down' and idx < last):
low = -2
m = tuple(oldX1.offsets).index(0)
oldX1.data = oldX1.data[m-high:m-low+1]
oldX1.offsets = oldX1.offsets[m-high:m-low+1]
# print "old D.todense()"
# fp(oldX1.D.todense())
# print "new D.todense()"
# fp(X1.D.todense())
# print
# print X1.shape, oldX1.shape
# print (X1.D.offsets, oldX1.offsets), "%s+%s (dv %i) idx %i" % (sch0, sch1, dv, idx)
assert X1.axis == axis
assert np.array_equal(X1.D.todense(), oldX1.todense()), "%s+%s (dv %i) idx %i" % (sch0, sch1, dv, idx)
assert np.array_equal(X1.D.offsets, oldX1.offsets), "%s+%s (dv %i) idx %i" % (sch0, sch1, dv, idx)
assert (X1.D.data.shape == oldX1.data.shape), "%s+%s (dv %i) idx %i" % (sch0, sch1, dv, idx)
assert np.array_equal(X1.D.data, oldX1.data), "%s+%s (dv %i) idx %i" % (sch0, sch1, dv, idx)
),
}
# schemes = {(1,) : ({"scheme": "center"}, {"scheme": "backward", "from" : flip_idx_var})}
utils.tic("Building FDE Engine")
# F = FDE.FiniteDifferenceEngineADI(G, coefficients=coeffs, boundaries=bounds, schemes=schemes, force_bandwidth=(-2, 2))
F = HestonFiniteDifferenceEngine(H, nspots=nspots, nvols=nvols, flip_idx_spot=flip_idx_spot, flip_idx_var=flip_idx_var)
utils.toc()
L1_ = []
R1_ = []
utils.tic("Building As(s):\t")
print "(Up/Down)wind from:", flip_idx_spot
As_ = utils.nonuniform_complete_coefficients(dss, up_or_down=up_or_down_spot, flip_idx=flip_idx_spot)[0]
Ass_ = utils.nonuniform_complete_coefficients(dss)[1]
# As_, Ass_ = utils.nonuniform_forward_coefficients(dss)
assert not np.isnan(As_.data).any()
assert not np.isnan(Ass_.data).any()
mu_sfunc = mu_s
gamma2_sfunc = gamma2_s
for j, v in enumerate(vars):
# Be careful not to overwrite our operators
As, Ass = As_.copy(), Ass_.copy()
m = 2
mu_s = H.interest_rate.value * spots
# mu_s = mu_sfunc(0, spots, v)
# gamma2_s = gamma2_sfunc(0, spots, v)
gamma2_s = 0.5 * v * spots ** 2
def setUp(self):
s1_enable = 1
s2_enable = 1
v1_enable = 1
v2_enable = 1
r_enable = 1
dirichlet_s = 1
dirichlet_v = 1
kappa = 1
r = 0.06
theta = 0.04
sigma = 0.4
rho = 0.6
spot_max = 1500.0
var_max = 13.0
nspots = 5
nvols = 5
spotdensity = 7.0 # infinity is linear?
varexp = 5
# TODO:!!!!XXX TODO XXX
# var_max = nvols-1
# spot_max = nspots-1
up_or_down_spot = 'up'
up_or_down_var = 'down'
flip_idx_spot = nspots // 2
flip_idx_var = nvols // 2
k = spot_max / 4.0
# spots = np.linspace(0, spot_max, nspots)
# vars = np.linspace(0, var_max, nvols)
spots = utils.sinh_space(k, spot_max, spotdensity, nspots)
vars = utils.exponential_space(0.00, 0.04, var_max, varexp, nvols)
def mu_s(t, *dim):
return r * dim[0] * s1_enable
def gamma2_s(t, *dim):
return 0.5 * dim[1] * dim[0]**2 * s2_enable
def mu_v(t, *dim):
return kappa * (theta - dim[1]) * v1_enable
def gamma2_v(t, *dim):
return 0.5 * sigma**2 * dim[1] * v2_enable
coeffs = {
(): lambda t: -r * r_enable,
(0, ): mu_s,
(0, 0): gamma2_s,
(1, ): mu_v,
(1, 1): gamma2_v,
(0, 1): lambda t, *dim: dim[0] * dim[1] * rho * sigma
}
bounds = {
# D: U = 0 VN: dU/dS = 1
(
0, ): ((0 if dirichlet_s else 1, lambda *args: 0.0),
(1, lambda *args: 1.0)),
# D: U = 0 Free boundary
(0, 0): ((0 if dirichlet_s else 1, lambda *args: 0.0),
(None, lambda *x: 1.0)),
# Free boundary at low variance
(
1, ): (
(None, lambda *x: None),
# (0.0, lambda t, *dim: 0),
# D intrinsic value at high variance
# (None, lambda *x: None)
(0 if dirichlet_v else 1,
lambda t, *dim: np.maximum(0.0, dim[0] - k))),
# # Free boundary
(1, 1): (
(1, lambda *x: 0),
# D intrinsic value at high variance
# (None, lambda *x: None)
(0 if dirichlet_v else 1,
lambda t, *dim: np.maximum(0.0, dim[0] - k)))
}
schemes = {}
schemes[(0, )] = ({
"scheme": "center"
}, {
"scheme": up_or_down_spot,
"from": flip_idx_spot
})
schemes[(1, )] = ({
"scheme": "center"
}, {
"scheme": up_or_down_var,
"from": flip_idx_var
})
dss = np.hstack((np.nan, np.diff(spots)))
dvs = np.hstack((np.nan, np.diff(vars)))
As_ = utils.nonuniform_complete_coefficients(
dss, up_or_down=up_or_down_spot, flip_idx=flip_idx_spot)[0]
Ass_ = utils.nonuniform_complete_coefficients(dss)[1]
L1_ = []
R1_ = []
# As_, Ass_ = utils.nonuniform_forward_coefficients(dss)
assert (not np.isnan(As_.data).any())
assert (not np.isnan(Ass_.data).any())
for j, v in enumerate(vars):
# Be careful not to overwrite operators
As, Ass = As_.copy(), Ass_.copy()
m = 2
mu_s = r * spots * s1_enable
gamma2_s = 0.5 * v * spots**2 * s2_enable
for i, z in enumerate(mu_s):
# print z, coeffs[0,](0, spots[i])
assert z == coeffs[0, ](0, spots[i])
for i, z in enumerate(gamma2_s):
# print z, coeffs[0,0](0, spots[i], v)
assert z == coeffs[0, 0](0, spots[i], v)
Rs = np.zeros(nspots)
Rs[-1] = 1
As.data[m - 2, 2:] *= mu_s[:-2]
As.data[m - 1, 1:] *= mu_s[:-1]
As.data[m, :] *= mu_s
As.data[m + 1, :-1] *= mu_s[1:]
As.data[m + 2, :-2] *= mu_s[2:]
Rs *= mu_s
Rss = np.zeros(nspots)
Rss[-1] = 2 * dss[-1] / dss[-1]**2
Ass.data[m + 1, -2] = 2 / dss[-1]**2
Ass.data[m, -1] = -2 / dss[-1]**2
Ass.data[m - 2, 2:] *= gamma2_s[:-2]
Ass.data[m - 1, 1:] *= gamma2_s[:-1]
Ass.data[m, :] *= gamma2_s
Ass.data[m + 1, :-1] *= gamma2_s[1:]
Ass.data[m + 2, :-2] *= gamma2_s[2:]
Rss *= gamma2_s
L1_.append(As.copy())
L1_[j].data += Ass.data
L1_[j].data[m, :] -= 0.5 * r * r_enable
L1_[j].data[m, 0] = 1 * dirichlet_s
R1_.append((Rs + Rss).copy())
R1_[j][0] = 0
L2_ = []
R2_ = []
Av_ = utils.nonuniform_complete_coefficients(dvs,
up_or_down=up_or_down_var,
flip_idx=flip_idx_var)[0]
Avv_ = utils.nonuniform_complete_coefficients(dvs)[1]
assert (not np.isnan(Av_.data).any())
assert (not np.isnan(Avv_.data).any())
for i, s in enumerate(spots):
mu_v = kappa * (theta - vars) * v1_enable
gamma2_v = 0.5 * sigma**2 * vars * v2_enable
# for j, z in enumerate(mu_v):
# assert z == coeffs[1,](0, 0, vars[j])
# for j, z in enumerate(gamma2_v):
# assert z == coeffs[1,1](0, 0, vars[j])
# Be careful not to overwrite our operators
Av, Avv = Av_.copy(), Avv_.copy()
m = 2
Av.data[m - 2, 2] = -dvs[1] / (dvs[2] * (dvs[1] + dvs[2]))
Av.data[m - 1, 1] = (dvs[1] + dvs[2]) / (dvs[1] * dvs[2])
Av.data[m,
0] = (-2 * dvs[1] - dvs[2]) / (dvs[1] * (dvs[1] + dvs[2]))
Av.data[m - 2, 2:] *= mu_v[:-2]
Av.data[m - 1, 1:] *= mu_v[:-1]
Av.data[m, :] *= mu_v
Av.data[m + 1, :-1] *= mu_v[1:]
Av.data[m + 2, :-2] *= mu_v[2:]
Rv = np.zeros(nvols)
Rv *= mu_v
Avv.data[m - 1, 1] = 2 / dvs[1]**2
Avv.data[m, 0] = -2 / dvs[1]**2
Avv.data[m - 2, 2:] *= gamma2_v[:-2]
Avv.data[m - 1, 1:] *= gamma2_v[:-1]
Avv.data[m, :] *= gamma2_v
Avv.data[m + 1, :-1] *= gamma2_v[1:]
Avv.data[m + 2, :-2] *= gamma2_v[2:]
Rvv = np.zeros(nvols)
Rvv[0] = 2 * dvs[1] / dvs[1]**2
Rvv *= gamma2_v
L2_.append(Av.copy())
L2_[i].data += Avv.data
L2_[i].data[m, :] -= 0.5 * r * r_enable
L2_[i].data[
m,
-1] = 1 * dirichlet_v # This is to cancel out the previous value so we can
# set the dirichlet boundary condition using R.
# Then we have U_i + -U_i + R
R2_.append(Rv + Rvv)
R2_[i][-1] = 0 # np.maximum(0, s - k)
def flatten_tensor(mats):
diags = np.hstack([x.data for x in mats])
flatmat = scipy.sparse.dia_matrix(
(diags, mats[0].offsets),
shape=(diags.shape[1], diags.shape[1]))
return flatmat
L1 = flatten_tensor(L1_)
L2 = flatten_tensor(L2_)
R1 = np.array(R1_).T
R2 = np.array(R2_)
self.As_ = As_
self.Ass_ = Ass_
self.L1_ = L1
self.R1_ = R1
self.L2_ = L2
self.R2_ = R2
# G = Grid.Grid((spots, vars), initializer=lambda x0,x1: np.maximum(x0-k,0))
self.G = Grid.Grid((spots, vars), initializer=lambda x0, x1: x0 * x1)
# print G
self.F = FD.FiniteDifferenceEngineADI(self.G,
coefficients=coeffs,
boundaries=bounds,
schemes=schemes,
force_bandwidth=None)
self.F.init()
def setUp(self):
s1_enable = 1
s2_enable = 1
v1_enable = 1
v2_enable = 1
r_enable = 1
dirichlet_s = 1
dirichlet_v = 1
kappa = 1
r = 0.06
theta = 0.04
sigma = 0.4
rho = 0.6
spot_max = 1500.0
var_max = 13.0
nspots = 5
nvols = 5
spotdensity = 7.0 # infinity is linear?
varexp = 5
# TODO:!!!!XXX TODO XXX
# var_max = nvols-1
# spot_max = nspots-1
up_or_down_spot = "up"
up_or_down_var = "down"
flip_idx_spot = nspots // 2
flip_idx_var = nvols // 2
k = spot_max / 4.0
# spots = np.linspace(0, spot_max, nspots)
# vars = np.linspace(0, var_max, nvols)
spots = utils.sinh_space(k, spot_max, spotdensity, nspots)
vars = utils.exponential_space(0.00, 0.04, var_max, varexp, nvols)
def mu_s(t, *dim):
return r * dim[0] * s1_enable
def gamma2_s(t, *dim):
return 0.5 * dim[1] * dim[0] ** 2 * s2_enable
def mu_v(t, *dim):
return kappa * (theta - dim[1]) * v1_enable
def gamma2_v(t, *dim):
return 0.5 * sigma ** 2 * dim[1] * v2_enable
coeffs = {
(): lambda t: -r * r_enable,
(0,): mu_s,
(0, 0): gamma2_s,
(1,): mu_v,
(1, 1): gamma2_v,
(0, 1): lambda t, *dim: dim[0] * dim[1] * rho * sigma,
}
bounds = {
# D: U = 0 VN: dU/dS = 1
(0,): ((0 if dirichlet_s else 1, lambda *args: 0.0), (1, lambda *args: 1.0)),
# D: U = 0 Free boundary
(0, 0): ((0 if dirichlet_s else 1, lambda *args: 0.0), (None, lambda *x: 1.0)),
# Free boundary at low variance
(1,): (
(None, lambda *x: None),
# (0.0, lambda t, *dim: 0),
# D intrinsic value at high variance
# (None, lambda *x: None)
(0 if dirichlet_v else 1, lambda t, *dim: np.maximum(0.0, dim[0] - k)),
),
# # Free boundary
(1, 1): (
(1, lambda *x: 0),
# D intrinsic value at high variance
# (None, lambda *x: None)
(0 if dirichlet_v else 1, lambda t, *dim: np.maximum(0.0, dim[0] - k)),
),
}
schemes = {}
schemes[(0,)] = ({"scheme": "center"}, {"scheme": up_or_down_spot, "from": flip_idx_spot})
schemes[(1,)] = ({"scheme": "center"}, {"scheme": up_or_down_var, "from": flip_idx_var})
dss = np.hstack((np.nan, np.diff(spots)))
dvs = np.hstack((np.nan, np.diff(vars)))
As_ = utils.nonuniform_complete_coefficients(dss, up_or_down=up_or_down_spot, flip_idx=flip_idx_spot)[0]
Ass_ = utils.nonuniform_complete_coefficients(dss)[1]
L1_ = []
R1_ = []
# As_, Ass_ = utils.nonuniform_forward_coefficients(dss)
assert not np.isnan(As_.data).any()
assert not np.isnan(Ass_.data).any()
for j, v in enumerate(vars):
# Be careful not to overwrite operators
As, Ass = As_.copy(), Ass_.copy()
m = 2
mu_s = r * spots * s1_enable
gamma2_s = 0.5 * v * spots ** 2 * s2_enable
for i, z in enumerate(mu_s):
# print z, coeffs[0,](0, spots[i])
assert z == coeffs[0,](0, spots[i])
for i, z in enumerate(gamma2_s):
# print z, coeffs[0,0](0, spots[i], v)
assert z == coeffs[0, 0](0, spots[i], v)
Rs = np.zeros(nspots)
Rs[-1] = 1
As.data[m - 2, 2:] *= mu_s[:-2]
As.data[m - 1, 1:] *= mu_s[:-1]
As.data[m, :] *= mu_s
As.data[m + 1, :-1] *= mu_s[1:]
As.data[m + 2, :-2] *= mu_s[2:]
Rs *= mu_s
Rss = np.zeros(nspots)
Rss[-1] = 2 * dss[-1] / dss[-1] ** 2
Ass.data[m + 1, -2] = 2 / dss[-1] ** 2
Ass.data[m, -1] = -2 / dss[-1] ** 2
Ass.data[m - 2, 2:] *= gamma2_s[:-2]
Ass.data[m - 1, 1:] *= gamma2_s[:-1]
Ass.data[m, :] *= gamma2_s
Ass.data[m + 1, :-1] *= gamma2_s[1:]
Ass.data[m + 2, :-2] *= gamma2_s[2:]
Rss *= gamma2_s
L1_.append(As.copy())
L1_[j].data += Ass.data
L1_[j].data[m, :] -= 0.5 * r * r_enable
L1_[j].data[m, 0] = 1 * dirichlet_s
R1_.append((Rs + Rss).copy())
R1_[j][0] = 0
L2_ = []
R2_ = []
Av_ = utils.nonuniform_complete_coefficients(dvs, up_or_down=up_or_down_var, flip_idx=flip_idx_var)[0]
Avv_ = utils.nonuniform_complete_coefficients(dvs)[1]
assert not np.isnan(Av_.data).any()
assert not np.isnan(Avv_.data).any()
for i, s in enumerate(spots):
mu_v = kappa * (theta - vars) * v1_enable
gamma2_v = 0.5 * sigma ** 2 * vars * v2_enable
# for j, z in enumerate(mu_v):
# assert z == coeffs[1,](0, 0, vars[j])
# for j, z in enumerate(gamma2_v):
# assert z == coeffs[1,1](0, 0, vars[j])
# Be careful not to overwrite our operators
Av, Avv = Av_.copy(), Avv_.copy()
m = 2
Av.data[m - 2, 2] = -dvs[1] / (dvs[2] * (dvs[1] + dvs[2]))
Av.data[m - 1, 1] = (dvs[1] + dvs[2]) / (dvs[1] * dvs[2])
Av.data[m, 0] = (-2 * dvs[1] - dvs[2]) / (dvs[1] * (dvs[1] + dvs[2]))
Av.data[m - 2, 2:] *= mu_v[:-2]
Av.data[m - 1, 1:] *= mu_v[:-1]
Av.data[m, :] *= mu_v
Av.data[m + 1, :-1] *= mu_v[1:]
Av.data[m + 2, :-2] *= mu_v[2:]
Rv = np.zeros(nvols)
Rv *= mu_v
Avv.data[m - 1, 1] = 2 / dvs[1] ** 2
Avv.data[m, 0] = -2 / dvs[1] ** 2
Avv.data[m - 2, 2:] *= gamma2_v[:-2]
Avv.data[m - 1, 1:] *= gamma2_v[:-1]
Avv.data[m, :] *= gamma2_v
Avv.data[m + 1, :-1] *= gamma2_v[1:]
Avv.data[m + 2, :-2] *= gamma2_v[2:]
Rvv = np.zeros(nvols)
Rvv[0] = 2 * dvs[1] / dvs[1] ** 2
Rvv *= gamma2_v
L2_.append(Av.copy())
L2_[i].data += Avv.data
L2_[i].data[m, :] -= 0.5 * r * r_enable
L2_[i].data[m, -1] = 1 * dirichlet_v # This is to cancel out the previous value so we can
# set the dirichlet boundary condition using R.
# Then we have U_i + -U_i + R
R2_.append(Rv + Rvv)
R2_[i][-1] = 0 # np.maximum(0, s - k)
def flatten_tensor(mats):
diags = np.hstack([x.data for x in mats])
flatmat = scipy.sparse.dia_matrix((diags, mats[0].offsets), shape=(diags.shape[1], diags.shape[1]))
return flatmat
L1 = flatten_tensor(L1_)
L2 = flatten_tensor(L2_)
R1 = np.array(R1_).T
R2 = np.array(R2_)
self.As_ = As_
self.Ass_ = Ass_
self.L1_ = L1
self.R1_ = R1
self.L2_ = L2
self.R2_ = R2
# G = Grid.Grid((spots, vars), initializer=lambda x0,x1: np.maximum(x0-k,0))
self.G = Grid.Grid((spots, vars), initializer=lambda x0, x1: x0 * x1)
# print G
self.F = FD.FiniteDifferenceEngineADI(
self.G, coefficients=coeffs, boundaries=bounds, schemes=schemes, force_bandwidth=None
)
self.F.init()