def test_BKExampleOne():
testCases.banner("=== HULL INITIAL EXAMPLE SECTION 28.7 ED 6 PG 668 ====")
times = [0.0, 0.5000, 1.00000, 1.50000, 2.00000, 2.500000, 3.00000]
zeros = [0.03, 0.0343, 0.03824, 0.04183, 0.04512, 0.048512, 0.05086]
times = np.array(times)
zeros = np.array(zeros)
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
end_date = Date(1, 6, 2021)
sigma = 0.25
a = 0.22
num_time_steps = 3
tmat = (end_date - start_date) / gDaysInYear
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
# Agrees with Figure 28.10 - Not exact as we have dt not exactly 0.50
if num_time_steps < 5:
testCases.header("LABEL", "VALUE")
testCases.print("QTREE", model._Q)
testCases.print("RTREE", model._rt)
# print_tree(model._rt)
testCases.print("PU AT LAST TIME", model._pu)
testCases.print("PDM AT LAST TIME", model._pm)
testCases.print("PD AT LAST TIME", model._pd)
def test_BKExampleOne():
times = [0.0, 0.5000, 1.00000, 1.50000, 2.00000, 2.500000, 3.00000]
zeros = [0.03, 0.0343, 0.03824, 0.04183, 0.04512, 0.048512, 0.05086]
times = np.array(times)
zeros = np.array(zeros)
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
end_date = Date(1, 6, 2021)
sigma = 0.25
a = 0.22
num_time_steps = 3
tmat = (end_date - start_date) / gDaysInYear
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
assert [round(x, 4) for x in model._Q[2]] == \
[0.0190, 0.2126, 0.5009, 0.2112, 0.0187]
assert [round(x, 4) for x in model._rt[2]] == \
[0.0259, 0.0351, 0.0477, 0.0648, 0.0881]
assert [round(x, 4) for x in model._pu] == \
[0.0808, 0.2278, 0.1667, 0.1177, 0.8606]
assert [round(x, 4) for x in model._pm] == \
[0.0586, 0.6545, 0.6667, 0.6545, 0.0586]
assert [round(x, 4) for x in model._pd] == \
[0.8606, 0.1177, 0.1667, 0.2278, 0.0808]
def test_BKExampleTwo():
# Valuation of a European option on a coupon bearing bond
# This follows example in Fig 28.11 of John Hull's book but does not
# have the exact same dt so there are some differences
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
expiry_date = settlement_date.add_tenor("18m")
maturity_date = settlement_date.add_tenor("10Y")
coupon = 0.05
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
num_flows = len(bond._flow_dates)
for i in range(1, num_flows):
pcd = bond._flow_dates[i - 1]
ncd = bond._flow_dates[i]
if pcd < settlement_date and ncd > settlement_date:
flow_time = (pcd - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
for flow_date in bond._flow_dates:
if flow_date > settlement_date:
flow_time = (flow_date - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
coupon_times = np.array(coupon_times)
coupon_flows = np.array(coupon_flows)
strike_price = 105.0
face = 100.0
tmat = (maturity_date - settlement_date) / gDaysInYear
texp = (expiry_date - settlement_date) / gDaysInYear
times = np.linspace(0, tmat, 11)
dates = settlement_date.add_years(times)
dfs = np.exp(-0.05 * times)
curve = DiscountCurve(settlement_date, dates, dfs)
price = bond.clean_price_from_discount_curve(settlement_date, curve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
sigma = 0.20
a = 0.05
num_time_steps = 26
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
exercise_type = FinExerciseTypes.AMERICAN
v = model.bond_option(texp, strike_price, face, coupon_times, coupon_flows,
exercise_type)
# Test convergence
num_steps_list = [100, 200, 300, 500, 1000]
exercise_type = FinExerciseTypes.AMERICAN
testCases.header("TIMESTEPS", "TIME", "VALUE")
treeVector = []
for num_time_steps in num_steps_list:
start = time.time()
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
v = model.bond_option(texp, strike_price, face, coupon_times,
coupon_flows, exercise_type)
end = time.time()
period = end - start
treeVector.append(v)
testCases.print(num_time_steps, period, v)
# plt.plot(num_steps_list, treeVector)
# Value in Hill converges to 0.699 with 100 time steps while I get 0.700
if 1 == 0:
print("RT")
print_tree(model._rt, 5)
print("Q")
print_tree(model._Q, 5)
def test_BKExampleTwo():
# Valuation of a European option on a coupon bearing bond
# This follows example in Fig 28.11 of John Hull's book but does not
# have the exact same dt so there are some differences
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
expiry_date = settlement_date.add_tenor("18m")
maturity_date = settlement_date.add_tenor("10Y")
coupon = 0.05
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
num_flows = len(bond._coupon_dates)
for i in range(1, num_flows):
pcd = bond._coupon_dates[i - 1]
ncd = bond._coupon_dates[i]
if pcd < settlement_date and ncd > settlement_date:
flow_time = (pcd - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
for flow_date in bond._coupon_dates:
if flow_date > settlement_date:
flow_time = (flow_date - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
coupon_times = np.array(coupon_times)
coupon_flows = np.array(coupon_flows)
strike_price = 105.0
face = 100.0
tmat = (maturity_date - settlement_date) / gDaysInYear
texp = (expiry_date - settlement_date) / gDaysInYear
times = np.linspace(0, tmat, 11)
dates = settlement_date.add_years(times)
dfs = np.exp(-0.05 * times)
curve = DiscountCurve(settlement_date, dates, dfs)
price = bond.clean_price_from_discount_curve(settlement_date, curve)
assert round(price, 4) == 99.5420
sigma = 0.20
a = 0.05
num_time_steps = 26
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
exercise_type = FinExerciseTypes.AMERICAN
v = model.bond_option(texp, strike_price, face, coupon_times, coupon_flows,
exercise_type)
# Test convergence
num_time_steps = 200
exercise_type = FinExerciseTypes.AMERICAN
treeVector = []
model = BKTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
v = model.bond_option(texp, strike_price, face, coupon_times, coupon_flows,
exercise_type)
treeVector.append(v)
assert round(v['call'], 4) == 0.6998
assert round(v['put'], 4) == 7.9605
