def main():
N = 80
S0 = 100
Sl = 0
Su = 200
model = BinomialModel(N, dS, payoff)
P = model.price(S0)
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
plot_H(ax, Sl, Su, model, P)
ax.set_ylim(Sl, Su)
ax.set_xlabel("Time")
ax.set_ylabel("Stock Price")
ax.set_zlabel("Default Cost after Hedging ($H^{c}_t$)")
def test_call(self):
"""Test that the binomial model correctly prices a call option."""
def price(r):
d1 = (np.log(100. / K) + r + 0.0005) / 0.1
d2 = d1 - 0.1
price = stats.norm.cdf(d1) * 100
price -= stats.norm.cdf(d2) * K * np.exp(-r)
return price
dS = WienerJumpProcess(0.1, 0.1)
dSdq = WienerJumpProcess(0.1, 0.1, 0.1)
accuracy = 10
step_down = set((59, 61, 64, 68, 72, 78, 83, 89, 100, 119))
step_up = set((136, 158, 172, 183, 193))
for K in range(1, 200):
if K in step_down:
accuracy -= 1
elif K in step_up:
accuracy += 1
V = CallE(1, K)
model = BinomialModel(128, dS, V)
self.assertAlmostEqual(float(model.price(100)), price(0.1), accuracy)
model = BinomialModel(128, dSdq, V)
self.assertAlmostEqual(float(model.price(100)), price(0.2), accuracy)
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())
def test_forward(self):
"""Test that the binomial model correctly prices a forward contract."""
dS = WienerJumpProcess(0.1, 0.1)
dSdq = WienerJumpProcess(0.1, 0.1, 0.02)
for K in range(200):
V = Forward(1, K)
model = BinomialModel(2, dS, V)
self.assertAlmostEqual(float(model.price(100)), 100 - K * np.exp(-0.1))
model = BinomialModel(2, dSdq, V)
self.assertAlmostEqual(float(model.price(100)), 100 - K * np.exp(-0.12))
def main():
S0 = 100
Sl = 0
Su = 200
X = range(11)
N = lambda x: 2**(x + 1) * T
K = lambda x: 2**((x + 1) // 2) * (Su - Sl)
fig = plt.figure()
fig.set_figwidth(1.8 * fig.get_figwidth())
plt_x = fig.add_subplot(1, 2, 1)
plt_t = fig.add_subplot(1, 2, 2)
p = []
t = []
for x in X:
start = time.time()
p.append(float(BinomialModel(N(x), dS, payoff).price(S0)))
t.append(time.time() - start)
plt_x.plot(X, p)
plt_t.plot(t, p)
print p[-1]
for scheme in (ImplicitScheme, CrankNicolsonScheme, PenaltyScheme):
p = []
t = []
for x in X:
k = K(x)
Sk = k * (S0 - Sl) / (Su - Sl)
start = time.time()
p.append(FDEModel(N(x), dS, payoff).price(Sl, Su, k, scheme=scheme).V[0][Sk])
t.append(time.time() - start)
plt_x.plot(X, p[:len(X)])
plt_t.plot(t, p)
print p[-1]
label(plt_x, "$\\delta_t = 2^{-(x + 1)}$; $\\delta_S = 2^{-\\frac{x + 1}{2}}$")
label(plt_t, "Computational Time (seconds)")
#plt_t.set_xlim(0, 2.5)
plt_t.set_xscale('log')
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))
