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_terminal(self):
"""Test value of terminal for American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.maximum(S - K, 0)
payoff = Time(CallE(T, K), (T,))
self.assertTrue((payoff.terminal(S) == V).all())
payoff = Time(CallE(T, K), ())
self.assertTrue((payoff.terminal(S) == np.zeros(S.shape)).all())
def test_transcient(self):
"""Test value of transient for American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
times = list(np.linspace(0, 1, N // 4, endpoint=False)) + [(0.5, 1)]
Vm = np.maximum(S - K, V)
payoff = Time(CallA(T, K), times)
for t in np.linspace(0, 1, N, endpoint=False):
if float(t) in times or t > 0.5:
self.assertTrue((payoff.transient(t, V, S) == Vm).all())
else:
self.assertTrue((payoff.transient(t, V, S) == V).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
def test_default(self):
"""Test default value of American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
times = list(np.linspace(0, 1, N // 4, endpoint=False)) + [(0.5, 1)]
Vd = np.maximum(S - K, 0)
Vo = np.zeros(S.shape)
payoff = Time(CallA(T, K), times)
for t in np.linspace(0, 1, N, endpoint=False):
if float(t) in times or t > 0.5:
self.assertTrue((payoff.default(t, S) == Vd).all())
else:
self.assertTrue((payoff.default(t, S) == Vo).all())
self.assertRaises(AssertionError, payoff.default, T, S)
def test_transcient(self):
"""Test value of transient for American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.linspace(S0 + 10, S0 - 10, 21)
times = list(np.linspace(0, 1, N // 4, endpoint=False)) + [(0.5, 1)]
Vm = np.maximum(S - K, V)
payoff = Time(CallA(T, K), times)
for t in np.linspace(0, 1, N, endpoint=False):
if float(t) in times or t > 0.5:
self.assertTrue((payoff.transient(t, V, S) == Vm).all())
else:
self.assertTrue((payoff.transient(t, V, S) == V).all())
self.assertRaises(AssertionError, payoff.transient, T, V, S)
def test_default(self):
"""Test default value of American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
times = list(np.linspace(0, 1, N // 4, endpoint=False)) + [(0.5, 1)]
Vd = np.maximum(S - K, 0)
Vo = np.zeros(S.shape)
payoff = Time(CallA(T, K), times)
for t in np.linspace(0, 1, N, endpoint=False):
if float(t) in times or t > 0.5:
self.assertTrue((payoff.default(t, S) == Vd).all())
else:
self.assertTrue((payoff.default(t, S) == Vo).all())
self.assertRaises(AssertionError, payoff.default, T, 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, -.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_terminal(self):
"""Test value of terminal for American call with time restrictions."""
S = np.linspace(S0 - 10, S0 + 10, 21)
V = np.maximum(S - K, 0)
payoff = Time(CallE(T, K), (T, ))
self.assertTrue((payoff.terminal(S) == V).all())
payoff = Time(CallE(T, K), ())
self.assertTrue((payoff.terminal(S) == np.zeros(S.shape)).all())
dS_typical = WienerJumpProcess(r=0.05, sigma=0.2, lambd_=0.02, eta=0.3) # Partial default (default = 0%) dS_partial = WienerJumpProcess(r=0.05, sigma=0.2, lambd_=0.02, eta=0) # No default dS = WienerJumpProcess(r=0.05, sigma=0.2) # Bond # 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
# Variable hazard (a=-1.2), total default
dS_var = WienerJumpProcess(r=0.05,
sigma=0.25,
lambd_=lambda S: 0.062 * (S / 50)**-0.5,
eta=1)
# Bond
# Nominal value = 100
# Semi-annual coupon = 4
# Recovery factor = 40%
A = Annuity(T, np.arange(0.5, T + 0.5, 0.5), C=4, N=100, R=0.4)
# 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 = CallA(T, 0)
# Bond component of convertible bond
B = Stack([A, P, C])
# Equity component of convertible bond
E = S