def test_coupon(self):
"""Test coupon value of annuity."""
payoff = Annuity(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
payoffI = AnnuityI(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
pay = True
for t in np.linspace(0, 1, N + 1):
if pay:
V = 1
else:
V = 0
pay = not pay
self.assertTrue(payoff.coupon(t) == V)
self.assertTrue(payoffI.coupon(t) == 0)
def test_coupon(self):
"""Test coupon value of annuity."""
payoff = Annuity(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
payoffI = AnnuityI(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
pay = True
for t in np.linspace(0, 1, N + 1):
if pay:
V = 1
else:
V = 0
pay = not pay
self.assertTrue(payoff.coupon(t) == V)
self.assertTrue(payoffI.coupon(t) == 0)
def setUp(self):
T = 9
B = Annuity(T, [8], 4, 100, 0.5)
P = Time(PutV(T, 105), [2, 4, 5, 6])
C = Time(CallVR(T, 110), [3, 4, 6, 7])
S = Time(CallA(T, 0), [1, 2, 3, 4, 9])
self.payoff = Stack([B, P, C, S])
Ssect = [
np.linspace(0, 0.25, 10),
np.linspace(0.25, -.25, 10),
np.linspace(-.25, 0.75, 10),
np.linspace(0.75, 1, 9, endpoint=False)
]
Vsect = [
np.linspace(0, -.25, 10),
np.linspace(-.25, 0.25, 10),
np.linspace(0.25, 0.50, 10),
np.linspace(0.50, 1, 9, endpoint=False)
]
Ssect = np.array(sum((list(i) for i in Ssect), []))
Vsect = np.array(sum((list(i) for i in Vsect), []))
critical = [10, 50, 100, 105, 110, 200]
S = []
V = []
for i in range(len(critical) - 1):
l, u = critical[i:i + 2]
lu = u - l
S.extend(Ssect * lu + l)
V.extend(Vsect * lu + l)
self.S = np.array(S)
self.V = np.array(V)
def test_transcient(self):
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
payoff = Annuity(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
payoffI = AnnuityI(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
pay = True
for t in np.linspace(0, 1, N, endpoint=False):
if pay:
C = 1
else:
C = 0
pay = not pay
self.assertTrue((payoff.transient(t, V, S) == V).all())
self.assertTrue((payoffI.transient(t, V, S) == V + C).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
self.assertRaises(AssertionError, payoffI.transient, T, V, S)
def test_transcient(self):
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
payoff = Annuity(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
payoffI = AnnuityI(T, np.linspace(0, 1, N // 2 + 1), 1, 10)
pay = True
for t in np.linspace(0, 1, N, endpoint=False):
if pay:
C = 1
else:
C = 0
pay = not pay
self.assertTrue((payoff.transient(t, V, S) == V).all())
self.assertTrue((payoffI.transient(t, V, S) == V + C).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
self.assertRaises(AssertionError, payoffI.transient, T, V, S)
def test_terminal(self):
"""Test terminal value of annuity."""
S = np.linspace(S0 - 10, S0 + 10, 21)
Vo = np.ones(S.shape) * 10
self.assertTrue((Annuity(T, (), 1, 10).terminal(S) == Vo).all())
self.assertTrue((AnnuityI(T, (), 1, 10).terminal(S) == Vo).all())
self.assertTrue((AnnuityI(T, (T, ), 1,
10).terminal(S) == Vo + 1).all())
def test_annuity(self):
"""Test the pricing of a series of payments."""
def price(r):
erdt = np.exp(-r)
i = 1 / erdt - 1
return (1 - erdt**(T * 2)) / i + 10 * erdt**(T * 2)
dS = WienerJumpProcess(0.1, 0.1)
dSdq = WienerJumpProcess(0.1, 0.1, 0.02)
# Semi-annual payments of 1
T = 10
V = Annuity(T, np.arange(0.5, T + 0.5, 0.5), 1, 10)
model = BinomialModel(T * 2, dS, V)
self.assertAlmostEqual(float(model.price(100)), price(0.05))
model = BinomialModel(T * 2, dSdq, V)
self.assertAlmostEqual(float(model.price(100)), price(0.06))
def test_annuity(self):
"""Test the pricing of a series of payments."""
def price(r):
erdt = np.exp(-r)
i = 1 / erdt - 1
return (1 - erdt**(T * 2)) / i + 10 * erdt**(T * 2)
dS = WienerJumpProcess(0.1, 0.1)
dSdq = WienerJumpProcess(0.1, 0.1, 0.02)
# Semi-annual payments of 1
T = 10
V = Annuity(T, np.arange(0.5, T + 0.5, 0.5), 1, 10)
model = FDEModel(T * 8, dS, V)
model2 = FDEModel(T * 8, dSdq, V)
for scheme in SCHEMES:
P = model.price(0, 200, 25, scheme=scheme)
self.assertTrue((np.abs(P.V[0] - price(0.05)) < 1e-1).all())
P = model2.price(0, 200, 25, scheme=scheme)
self.assertTrue((np.abs(P.V[0] - price(0.06)) < 1e-1).all())
def test_value(self):
"""Test the value object for the finite difference model."""
dS = WienerJumpProcess(0.1, 0.1, 0.02, 0)
N = 16
T = 1
ct = np.linspace(0, T, N // 2 + 1)
c = 1
Sl = 0
Su = 200
K = 40
model = FDEModel(N, dS, Stack([CallA(T, 100), Annuity(T, ct, c)]))
P = model.price(Sl, Su, K)
S = P.S
# Test N
self.assertEqual(P.N, N)
# Test time series
self.assertEqual(P.t[0], 0)
self.assertEqual(P.t[-1], T)
self.assertEqual(len(P.t), N + 1)
# Test Coupon sequence
self.assertTrue((P.C[::2] == c).all())
self.assertTrue((P.C[1::2] == 0).all())
# Test K
self.assertEqual(P.K, K)
# Test Stock series
self.assertEqual(P.S[0], Sl)
self.assertEqual(P.S[-1], Su)
self.assertEqual(len(P.S), K + 1)
# Test default sequence
self.assertEqual(len(P.V), N + 1)
for i in range(1, N + 1):
self.assertLessEqual(P.V[i][0] - P.C[i], P.V[i - 1][0])
self.assertLessEqual(P.V[i][-1] - P.C[i], P.V[i - 1][-1])
self.assertTrue((P.V[i][:-1] - 1e14 <= P.V[i][1:]).all())
self.assertEqual(len(P.X), N)
for i in range(1, N):
self.assertGreaterEqual(P.X[i][0], P.X[i - 1][0])
self.assertLessEqual(P.X[i][-1], P.X[i - 1][-1])
self.assertTrue((P.X[i][:-1] <= P.X[i][1:]).all())
def test_value(self):
"""Test the value object for the binomial model."""
dS = WienerJumpProcess(0.1, 0.1, 0.02, 0)
N = 16
T = 1
ct = np.linspace(0, T, N // 2 + 1)
c = 1
S = 100
model = BinomialModel(N, dS, Stack([CallA(T, S), Annuity(T, ct, c)]))
P = model.price(S)
# Test N
self.assertEqual(P.N, N)
# Test time series
self.assertEqual(P.t[0], 0)
self.assertEqual(P.t[-1], T)
self.assertEqual(len(P.t), N + 1)
# Test Coupon sequence
self.assertTrue((P.C[::2] == c).all())
self.assertTrue((P.C[1::2] == 0).all())
# Test price sequence
self.assertEqual(P.S[0][0], S)
self.assertEqual(len(P.S), N + 1)
for i in range(1, N + 1):
self.assertGreaterEqual(P.S[i][0], P.S[i - 1][0])
self.assertLessEqual(P.S[i][-1], P.S[i - 1][-1])
self.assertTrue((P.S[i][:-1] > P.S[i][1:]).all())
# Test default sequence
self.assertEqual(len(P.V), N + 1)
for i in range(1, N + 1):
self.assertGreaterEqual(P.V[i][0] - P.C[i], P.V[i - 1][0])
self.assertLessEqual(P.V[i][-1] - P.C[i], P.V[i - 1][-1])
self.assertTrue((P.V[i][:-1] >= P.V[i][1:]).all())
self.assertEqual(len(P.X), N)
for i in range(1, N):
self.assertGreaterEqual(P.X[i][0], P.X[i - 1][0])
self.assertLessEqual(P.X[i][-1], P.X[i - 1][-1])
self.assertTrue((P.X[i][:-1] >= P.X[i][1:]).all())