def test_BDTExampleThree():
# Valuation of a swaption as in Leif Andersen's paper - see Table 1 on
# SSRN-id155208.pdf
testCases.banner("===================== ANDERSEN PAPER ==============")
# This is a sanity check
testBlackModelCheck()
settlement_date = Date(1, 1, 2020)
times = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
dates = settlement_date.add_years(times)
rate = 0.06
dfs = 1.0 / (1.0 + rate / 2.0)**(2.0 * times)
curve = DiscountCurve(settlement_date, dates, dfs)
coupon = 0.06
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
strike_price = 100.0
face = 100.0
# Andersen paper
num_time_steps = 200
testCases.header("ExerciseType", "Sigma", "NumSteps", "Texp", "Tmat",
"V_Fixed", "V_pay", "V_rec")
for exercise_type in [
FinExerciseTypes.EUROPEAN, FinExerciseTypes.BERMUDAN
]:
for years_to_maturity in [4.0, 5.0, 10.0, 20.0]:
maturity_date = settlement_date.add_years(years_to_maturity)
issue_date = Date(maturity_date._d, maturity_date._m, 2000)
if years_to_maturity == 4.0 or years_to_maturity == 5.0:
sigma = 0.2012
elif years_to_maturity == 10.0:
sigma = 0.1522
elif years_to_maturity == 20.0:
sigma = 0.1035
for expiryYears in range(
int(years_to_maturity / 2) - 1, int(years_to_maturity)):
expiry_date = settlement_date.add_years(expiryYears)
tmat = (maturity_date - settlement_date) / gDaysInYear
texp = (expiry_date - settlement_date) / gDaysInYear
bond = Bond(issue_date, maturity_date, coupon, freq_type,
accrual_type)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
for flow_date in bond._flow_dates:
if flow_date > expiry_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)
price = bond.clean_price_from_discount_curve(
settlement_date, curve)
model = BDTTree(sigma, num_time_steps)
model.build_tree(tmat, times, dfs)
v = model.bermudan_swaption(texp, tmat, strike_price, face,
coupon_times, coupon_flows,
exercise_type)
testCases.print("%s" % exercise_type, "%9.5f" % sigma,
"%9.5f" % num_time_steps,
"%9.5f" % expiryYears,
"%9.5f" % years_to_maturity, "%9.5f" % price,
"%9.2f" % (v['pay'] * 100.0),
"%9.2f" % (v['rec'] * 100.0))
def test_BDTExampleThree():
# Valuation of a swaption as in Leif Andersen's paper - see Table 1 on
# SSRN-id155208.pdf
settlement_date = Date(1, 1, 2020)
times = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
dates = settlement_date.add_years(times)
rate = 0.06
dfs = 1.0 / (1.0 + rate / 2.0)**(2.0 * times)
curve = DiscountCurve(settlement_date, dates, dfs)
coupon = 0.06
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
strike_price = 100.0
face = 100.0
# Andersen paper
num_time_steps = 200
exercise_type = FinExerciseTypes.EUROPEAN
years_to_maturity = 4.0
expiryYears = 2.0
maturity_date = settlement_date.add_years(years_to_maturity)
issue_date = Date(maturity_date._d, maturity_date._m, 2000)
sigma = 0.2012
expiry_date = settlement_date.add_years(expiryYears)
tmat = (maturity_date - settlement_date) / gDaysInYear
texp = (expiry_date - settlement_date) / gDaysInYear
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
for flow_date in bond._coupon_dates:
if flow_date > expiry_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)
price = bond.clean_price_from_discount_curve(settlement_date, curve)
model = BDTTree(sigma, num_time_steps)
model.build_tree(tmat, times, dfs)
v = model.bermudan_swaption(texp, tmat, strike_price, face, coupon_times,
coupon_flows, exercise_type)
assert round(price, 5) == 100.01832
assert round(v['pay'] * 100, 2) == 0.00
assert round(v['rec'] * 100, 2) == 8883.21
exercise_type = FinExerciseTypes.BERMUDAN
years_to_maturity = 10.0
expiryYears = 5.0
maturity_date = settlement_date.add_years(years_to_maturity)
issue_date = Date(maturity_date._d, maturity_date._m, 2000)
sigma = 0.1522
expiry_date = settlement_date.add_years(expiryYears)
tmat = (maturity_date - settlement_date) / gDaysInYear
texp = (expiry_date - settlement_date) / gDaysInYear
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
for flow_date in bond._coupon_dates:
if flow_date > expiry_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)
price = bond.clean_price_from_discount_curve(settlement_date, curve)
model = BDTTree(sigma, num_time_steps)
model.build_tree(tmat, times, dfs)
v = model.bermudan_swaption(texp, tmat, strike_price, face, coupon_times,
coupon_flows, exercise_type)
assert round(price, 5) == 100.08625
assert round(v['pay'] * 100, 2) == 263.28
assert round(v['rec'] * 100, 2) == 7437.00