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_HullWhiteBondOption():
# Valuation of a European option on a coupon bearing bond
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 ncd > settlement_date:
if len(coupon_times) == 0:
flow_time = (pcd - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
flow_time = (ncd - 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 = 100.0
face = 100.0
y = 0.05
times = np.linspace(0, 10, 21)
dfs = np.power(1 + y / 2, -times * 2)
sigma = 0.0000001
a = 0.1
model = HWTree(sigma, a, None)
# Test convergence
num_steps_list = range(50, 500, 50)
texp = (expiry_date - settlement_date) / gDaysInYear
vJam = model.european_bond_option_jamshidian(texp, strike_price, face,
coupon_times, coupon_flows,
times, dfs)
testCases.banner(
"Pricing bond option on tree that goes to bond maturity and one using european bond option tree that goes to expiry."
)
testCases.header("NUMSTEPS", "TIME", "EXPIRY_ONLY", "EXPIRY_TREE",
"JAMSHIDIAN")
for num_time_steps in num_steps_list:
start = time.time()
model = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
model.build_tree(texp, times, dfs)
exercise_type = FinExerciseTypes.EUROPEAN
v1 = model.bond_option(texp, strike_price, face, coupon_times,
coupon_flows, exercise_type)
model = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_TREE)
model.build_tree(texp, times, dfs)
v2 = model.bond_option(texp, strike_price, face, coupon_times,
coupon_flows, exercise_type)
end = time.time()
period = end - start
testCases.print(num_time_steps, period, v1, v2, vJam)
# plt.plot(num_steps_list, treeVector)
if 1 == 0:
print("RT")
print_tree(model._rt, 5)
print("BOND")
print_tree(model._bond_values, 5)
print("OPTION")
print_tree(model._option_values, 5)