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_default(self):
"""Test default value of stacked Forward and American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
Vd = np.maximum(S - K, 0)
payoff = Stack([Forward(T, K), CallA(T, K)])
for t in np.linspace(0, 1, N, endpoint=False):
self.assertTrue((payoff.default(t, S) == Vd).all())
self.assertRaises(AssertionError, payoff.default, T, S)
def test_default(self):
"""Test default value of stacked Forward and American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
Vd = np.maximum(S - K, 0)
payoff = Stack([Forward(T, K), CallA(T, K)])
for t in np.linspace(0, 1, N, endpoint=False):
self.assertTrue((payoff.default(t, S) == Vd).all())
self.assertRaises(AssertionError, payoff.default, T, S)
def test_transcient(self):
"""Test value of transient for stacked normal and reversed American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
Vm = np.minimum(np.maximum(V, np.maximum(S - K, 0)), K + 5)
payoff = Stack([CallA(T, K), CallVR(T, K + 5)])
for t in np.linspace(0, 1, N, endpoint=False):
self.assertTrue((payoff.transient(t, V, S) == Vm).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
def test_transcient(self):
"""Test value of transient for stacked normal and reversed American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
Vm = np.minimum(np.maximum(V, np.maximum(S - K, 0)), K + 5)
payoff = Stack([CallA(T, K), CallVR(T, K + 5)])
for t in np.linspace(0, 1, N, endpoint=False):
self.assertTrue((payoff.transient(t, V, S) == Vm).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
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, -0.25, 10),
np.linspace(-0.25, 0.75, 10),
np.linspace(0.75, 1, 9, endpoint=False),
]
Vsect = [
np.linspace(0, -0.25, 10),
np.linspace(-0.25, 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_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())
# Nominal value = 100 # Semi-annual coupon = 4 # Recovery factor = 0 A = Annuity(T, np.arange(0.5, T + 0.5, 0.5), C=4, N=100, R=0) # American put option on portfolio # Strike = 105 # Time = 3 P = Time(Put(T, 105, A), times=[3]) # Reversed American call option on portfolio # Strike = 110 # Time = [2, 5] C = Time(Call(T, 110, A), times=[(2, 5)]) # Stock option (conversion option into stock for portfolio) S = Time(CallA(T, 0), times=[(0, 5)]) # Bond component of convertible bond B = Stack([A, P, C]) # Equity component of convertible bond E = S # Convertible bond: # Bond # American put option on portfolio # Reversed American call option on portfolio # Stock payoff = Stack([A, P, C, S])
class TestConvertibleBond(unittest.TestCase):
"""Test Payoff of unit tests, based on AKW08 Table 1"""
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_SV(self):
"""Test sample stock and portfolio values."""
S = self.S
V = self.V
for i in [50, 100, 105, 110]:
self.assertTrue((S > i).any())
self.assertTrue((S == i).any())
self.assertTrue((S < i).any())
self.assertTrue((V > i).any())
self.assertTrue((V == i).any())
self.assertTrue((V < i).any())
self.assertTrue(((S > i) & (V < i)).any())
self.assertTrue(((S < i) & (V > i)).any())
def test_conv(self):
"""Test conversion option, without call or put option."""
t = 1
S = self.S
V = self.V
Vm = np.maximum(V, S)
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_put(self):
"""Test conversion and put option without call option."""
t = 2
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Put option
put = (V < 105) & (S < 105)
self.assertTrue(put.any())
Vm[put] = 105
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_call(self):
"""Test conversion and call option, without put option."""
t = 3
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Call option
call = (V > 110) & (S <= 110)
Vm[call] = 110
self.assertTrue(call.any())
# Conversion option (forced conversion)
conv = (V > 110) & (S > 110) & (V > S)
self.assertTrue(conv.any())
Vm[conv] = S[conv]
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_call_put(self):
"""Test conversion, call and put option,"""
t = 4
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Put option
put = (V < 105) & (S < 105)
self.assertTrue(put.any())
Vm[put] = 105
# Call option
call = (V > 110) & (S <= 110)
Vm[call] = 110
self.assertTrue(call.any())
# Conversion option (forced conversion)
conv = (V > 110) & (S > 110) & (V > S)
self.assertTrue(conv.any())
Vm[conv] = S[conv]
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
# Default
Vd = np.maximum(S, 50)
self.assertTrue((self.payoff.default(t, S) == Vd).all())
def test_put(self):
"""Test put option, without conversion or call option."""
t = 5
S = self.S
V = self.V
Vm = np.maximum(V, 105)
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_put_call(self):
"""Test put and call option, without conversion option."""
t = 6
S = self.S
V = self.V
Vm = V.copy()
# Put option
put = (V < 105)
Vm[put] = 105
# Call option
call = (V > 110)
Vm[call] = 110
self.assertTrue(call.any())
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_call(self):
"""Test call option, without conversion or put option."""
t = 7
S = self.S
V = self.V
Vm = np.minimum(V, 110)
self.assertTrue((V > 110).any())
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_coupon(self):
t = 8
self.assertTrue((self.payoff.coupon(t) == 4).all())
def test_redemption(self):
"""Test redemption of convertible bond."""
S = self.S
V = np.maximum(100, S)
self.assertTrue((self.payoff.terminal(S) == V).all())
def test_terminal(self):
"""Test value of terminal for stacked Forward and American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.maximum(S - K + 5, 0)
payoff = Stack([Forward(T, K - 5), CallE(T, K)])
self.assertTrue((payoff.terminal(S) == V).all())
class TestConvertibleBond(unittest.TestCase):
"""Test Payoff of unit tests, based on AKW08 Table 1"""
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, -0.25, 10),
np.linspace(-0.25, 0.75, 10),
np.linspace(0.75, 1, 9, endpoint=False),
]
Vsect = [
np.linspace(0, -0.25, 10),
np.linspace(-0.25, 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_SV(self):
"""Test sample stock and portfolio values."""
S = self.S
V = self.V
for i in [50, 100, 105, 110]:
self.assertTrue((S > i).any())
self.assertTrue((S == i).any())
self.assertTrue((S < i).any())
self.assertTrue((V > i).any())
self.assertTrue((V == i).any())
self.assertTrue((V < i).any())
self.assertTrue(((S > i) & (V < i)).any())
self.assertTrue(((S < i) & (V > i)).any())
def test_conv(self):
"""Test conversion option, without call or put option."""
t = 1
S = self.S
V = self.V
Vm = np.maximum(V, S)
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_put(self):
"""Test conversion and put option without call option."""
t = 2
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Put option
put = (V < 105) & (S < 105)
self.assertTrue(put.any())
Vm[put] = 105
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_call(self):
"""Test conversion and call option, without put option."""
t = 3
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Call option
call = (V > 110) & (S <= 110)
Vm[call] = 110
self.assertTrue(call.any())
# Conversion option (forced conversion)
conv = (V > 110) & (S > 110) & (V > S)
self.assertTrue(conv.any())
Vm[conv] = S[conv]
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_conv_call_put(self):
"""Test conversion, call and put option,"""
t = 4
S = self.S
V = self.V
Vm = np.maximum(V, S) # Normal conversion
# Put option
put = (V < 105) & (S < 105)
self.assertTrue(put.any())
Vm[put] = 105
# Call option
call = (V > 110) & (S <= 110)
Vm[call] = 110
self.assertTrue(call.any())
# Conversion option (forced conversion)
conv = (V > 110) & (S > 110) & (V > S)
self.assertTrue(conv.any())
Vm[conv] = S[conv]
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
# Default
Vd = np.maximum(S, 50)
self.assertTrue((self.payoff.default(t, S) == Vd).all())
def test_put(self):
"""Test put option, without conversion or call option."""
t = 5
S = self.S
V = self.V
Vm = np.maximum(V, 105)
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_put_call(self):
"""Test put and call option, without conversion option."""
t = 6
S = self.S
V = self.V
Vm = V.copy()
# Put option
put = V < 105
Vm[put] = 105
# Call option
call = V > 110
Vm[call] = 110
self.assertTrue(call.any())
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_call(self):
"""Test call option, without conversion or put option."""
t = 7
S = self.S
V = self.V
Vm = np.minimum(V, 110)
self.assertTrue((V > 110).any())
self.assertTrue((self.payoff.transient(t, V, S) == Vm).all())
def test_coupon(self):
t = 8
self.assertTrue((self.payoff.coupon(t) == 4).all())
def test_redemption(self):
"""Test redemption of convertible bond."""
S = self.S
V = np.maximum(100, S)
self.assertTrue((self.payoff.terminal(S) == V).all())
def test_terminal(self):
"""Test value of terminal for stacked Forward and American call."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.maximum(S - K + 5, 0)
payoff = Stack([Forward(T, K - 5), CallE(T, K)])
self.assertTrue((payoff.terminal(S) == V).all())