def test_BondOptionAmericanConvergenceONE():
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date, 0.05)
# Bond details
maturity_date = Date(1, 9, 2025)
issue_date = Date(1, 9, 2016)
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)
# Option Details
expiry_date = Date(1, 12, 2020)
strike_price = 100.0
face = 100.0
testCases.header("TIME", "N", "PUT_AMER", "PUT_EUR", "CALL_AME",
"CALL_EUR")
timeSteps = range(20, 100, 20)
for num_time_steps in timeSteps:
sigma = 0.20
a = 0.1
start = time.time()
option_type = OptionTypes.AMERICAN_PUT
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = BKTree(sigma, a, num_time_steps)
v1put = bond_option1.value(settlement_date, discount_curve, model1)
option_type = OptionTypes.EUROPEAN_PUT
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = BKTree(sigma, a, num_time_steps)
v2put = bond_option2.value(settlement_date, discount_curve, model2)
option_type = OptionTypes.AMERICAN_CALL
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = BKTree(sigma, a, num_time_steps)
v1call = bond_option1.value(settlement_date, discount_curve, model1)
option_type = OptionTypes.EUROPEAN_CALL
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = BKTree(sigma, a, num_time_steps)
v2call = bond_option2.value(settlement_date, discount_curve, model2)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v1put, v2put, v1call, v2call)
def testIborSwaptionModels():
##########################################################################
# COMPARISON OF MODELS
##########################################################################
valuation_date = Date(1, 1, 2011)
libor_curve = test_ibor_depositsAndSwaps(valuation_date)
exercise_date = Date(1, 1, 2012)
swapMaturityDate = Date(1, 1, 2017)
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
strikes = np.linspace(0.02, 0.08, 5)
testCases.header("LAB", "STRIKE", "BLK", "BLK_SHFT", "SABR", "SABR_SHFT",
"HW", "BK")
model1 = Black(0.00001)
model2 = BlackShifted(0.00001, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.00001, 0.00001)
model6 = BKTree(0.01, 0.01)
settlement_date = valuation_date.add_weekdays(2)
for k in strikes:
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, swaptionType, k,
swapFixedFrequencyType, swapFixedDayCountType)
swap1 = swaption.value(valuation_date, libor_curve, model1)
swap2 = swaption.value(valuation_date, libor_curve, model2)
swap3 = swaption.value(valuation_date, libor_curve, model3)
swap4 = swaption.value(valuation_date, libor_curve, model4)
swap5 = swaption.value(valuation_date, libor_curve, model5)
swap6 = swaption.value(valuation_date, libor_curve, model6)
testCases.print("PAY", k, swap1, swap2, swap3, swap4, swap5, swap6)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BK")
for k in strikes:
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, swaptionType, k,
swapFixedFrequencyType, swapFixedDayCountType)
swap1 = swaption.value(valuation_date, libor_curve, model1)
swap2 = swaption.value(valuation_date, libor_curve, model2)
swap3 = swaption.value(valuation_date, libor_curve, model3)
swap4 = swaption.value(valuation_date, libor_curve, model4)
swap5 = swaption.value(valuation_date, libor_curve, model5)
swap6 = swaption.value(valuation_date, libor_curve, model6)
testCases.print("REC", k, swap1, swap2, swap3, swap4, swap5, swap6)
def test_matlab_bk():
sigma = 0.01 # This volatility is very small for a BK process
a = 0.1
model = BKTree(sigma, a, num_time_steps)
v = puttableBond_matlab.value(settlement_date_matlab,
discount_curve_matlab, model)
assert round(v['bondwithoption'], 4) == 102.3508
assert round(v['bondpure'], 4) == 102.0603
def test_quantlib_bk():
sigma = 0.12 / 0.035 # basis point volatility
a = 0.03
model = BKTree(sigma, a, num_time_steps)
v = puttableBond_quantlib.value(settlement_date_quantlib,
discount_curve_quantlib, model)
assert round(v['bondwithoption'], 4) == 89.7614
assert round(v['bondpure'], 4) == 95.0619
def test_bk_bermudan_exercise():
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = BKTree(sigma, a, num_time_steps)
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
assert round(valuePay, 4) == 6313.7455
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
assert valueRec == 0.0
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = BKTree(sigma, a, num_time_steps)
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
assert round(valuePay, 4) == 19175.5406
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
assert round(valueRec, 4) == 12956.6057
def test_american_put_bk():
option_type = OptionTypes.AMERICAN_PUT
strike_price = 100
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
sigma = 0.02
a = 0.1
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
assert round(v, 4) == 0.5331
def test_european_call_bk():
option_type = OptionTypes.EUROPEAN_CALL
strike_price = 100
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
sigma = 0.20
a = 0.1
num_time_steps = 20
model = BKTree(sigma, a, num_time_steps)
v = bond_option.value(settlement_date, discount_curve, model)
assert round(v, 4) == 1.7055
def test_BondOptionAmericanConvergenceTWO():
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date,
0.05,
FrequencyTypes.CONTINUOUS)
# Bond details
issue_date = Date(1, 9, 2014)
maturity_date = Date(1, 9, 2025)
coupon = 0.05
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
expiry_date = settlement_date.add_tenor("18m")
face = 100.0
spotValue = bond.full_price_from_discount_curve(
settlement_date, discount_curve)
testCases.header("LABEL", "VALUE")
testCases.print("BOND PRICE", spotValue)
testCases.header("TIME", "N", "EUR_CALL", "AMER_CALL",
"EUR_PUT", "AMER_PUT")
sigma = 0.2
a = 0.1
bkModel = BKTree(sigma, a)
K = 101.0
vec_ec = []
vec_ac = []
vec_ep = []
vec_ap = []
if 1 == 1:
K = 100.0
bkModel = BKTree(sigma, a, 100)
europeanCallBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlement_date, discount_curve,
bkModel)
testCases.header("LABEL", "VALUE")
testCases.print("OPTION", v_ec)
num_stepsVector = range(100, 100, 1) # should be 100-400
for num_steps in num_stepsVector:
bkModel = BKTree(sigma, a, num_steps)
start = time.time()
europeanCallBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlement_date, discount_curve,
bkModel)
americanCallBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.AMERICAN_CALL)
v_ac = americanCallBondOption.value(settlement_date, discount_curve,
bkModel)
europeanPutBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.EUROPEAN_PUT)
v_ep = europeanPutBondOption.value(settlement_date, discount_curve,
bkModel)
americanPutBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.AMERICAN_PUT)
v_ap = americanPutBondOption.value(settlement_date, discount_curve,
bkModel)
end = time.time()
period = end - start
testCases.print(period, num_steps, v_ec, v_ac, v_ep, v_ap)
vec_ec.append(v_ec)
vec_ac.append(v_ac)
vec_ep.append(v_ep)
vec_ap.append(v_ap)
if plotGraphs:
plt.figure()
plt.plot(num_stepsVector, vec_ec, label="European Call")
plt.legend()
plt.figure()
plt.plot(num_stepsVector, vec_ac, label="American Call")
plt.legend()
plt.figure()
plt.plot(num_stepsVector, vec_ep, label="European Put")
plt.legend()
plt.figure()
plt.plot(num_stepsVector, vec_ap, label="American Put")
plt.legend()
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 testIborSwaptionMatlabExamples():
# We value a European swaption using Black's model and try to replicate a
# ML example at https://fr.mathworks.com/help/fininst/swaptionbyblk.html
testCases.header("=======================================")
testCases.header("MATLAB EXAMPLE WITH FLAT TERM STRUCTURE")
testCases.header("=======================================")
valuation_date = Date(1, 1, 2010)
libor_curve = DiscountCurveFlat(valuation_date, 0.06,
FrequencyTypes.CONTINUOUS,
DayCountTypes.THIRTY_E_360)
settlement_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2016)
maturity_date = Date(1, 1, 2019)
fixed_coupon = 0.062
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
# Pricing a PAY
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = Black(0.20)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.071
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH TERM STRUCTURE")
testCases.header("===================================")
valuation_date = Date(1, 1, 2010)
dates = [
Date(1, 1, 2011),
Date(1, 1, 2012),
Date(1, 1, 2013),
Date(1, 1, 2014),
Date(1, 1, 2015)
]
zero_rates = [0.03, 0.034, 0.037, 0.039, 0.040]
contFreq = FrequencyTypes.CONTINUOUS
interp_type = InterpTypes.LINEAR_ZERO_RATES
day_count_type = DayCountTypes.THIRTY_E_360
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2012)
maturity_date = Date(1, 1, 2017)
fixed_coupon = 0.03
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360
float_frequency_type = FrequencyTypes.SEMI_ANNUAL
float_day_count_type = DayCountTypes.THIRTY_E_360
notional = 1000.0
# Pricing a put
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional,
float_frequency_type, float_day_count_type)
model = Black(0.21)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.5771
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH SHIFTED BLACK")
testCases.header("===================================")
valuation_date = Date(1, 1, 2016)
dates = [
Date(1, 1, 2017),
Date(1, 1, 2018),
Date(1, 1, 2019),
Date(1, 1, 2020),
Date(1, 1, 2021)
]
zero_rates = np.array([-0.02, 0.024, 0.047, 0.090, 0.12]) / 100.0
contFreq = FrequencyTypes.ANNUAL
interp_type = InterpTypes.LINEAR_ZERO_RATES
day_count_type = DayCountTypes.THIRTY_E_360
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = Date(1, 1, 2016)
exercise_date = Date(1, 1, 2017)
maturity_date = Date(1, 1, 2020)
fixed_coupon = -0.003
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
float_frequency_type = FrequencyTypes.SEMI_ANNUAL
float_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 1000.0
# Pricing a PAY
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional,
float_frequency_type, float_day_count_type)
model = BlackShifted(0.31, 0.008)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 12.8301
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH HULL WHITE")
testCases.header("===================================")
# https://fr.mathworks.com/help/fininst/swaptionbyhw.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.075] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.SEMI_ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2010)
maturity_date = Date(1, 1, 2012)
fixed_coupon = 0.04
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = HWTree(0.05, 0.01)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.9201
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("====================================")
testCases.header("MATLAB EXAMPLE WITH BLACK KARASINSKI")
testCases.header("====================================")
# https://fr.mathworks.com/help/fininst/swaptionbybk.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.07] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.SEMI_ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2011)
maturity_date = Date(1, 1, 2012)
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
model = BKTree(0.1, 0.05, 200)
fixed_coupon = 0.07
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.3634
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
fixed_coupon = 0.0725
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.4798
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("====================================")
testCases.header("MATLAB EXAMPLE WITH BLACK-DERMAN-TOY")
testCases.header("====================================")
# https://fr.mathworks.com/help/fininst/swaptionbybdt.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.06] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2012)
maturity_date = Date(1, 1, 2015)
fixed_frequency_type = FrequencyTypes.ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
fixed_coupon = 0.062
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = BDTTree(0.20, 200)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.0592
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
def test_IborBermudanSwaptionBKModel():
""" Replicate examples in paper by Leif Andersen which can be found at
file:///C:/Users/Dominic/Downloads/SSRN-id155208.pdf """
valuation_date = Date(1, 1, 2011)
settlement_date = valuation_date
exercise_date = settlement_date.add_years(1)
swapMaturityDate = settlement_date.add_years(4)
swapFixedCoupon = 0.060
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
libor_curve = DiscountCurveFlat(valuation_date, 0.0625,
FrequencyTypes.SEMI_ANNUAL,
DayCountTypes.ACT_365F)
fwdPAYSwap = IborSwap(exercise_date, swapMaturityDate, SwapTypes.PAY,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fwdSwapValue = fwdPAYSwap.value(settlement_date, libor_curve, libor_curve)
testCases.header("LABEL", "VALUE")
testCases.print("FWD SWAP VALUE", fwdSwapValue)
# fwdPAYSwap.print_fixed_leg_pv()
# Now we create the European swaptions
fixed_leg_type = SwapTypes.PAY
europeanSwaptionPay = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, fixed_leg_type,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
europeanSwaptionRec = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, fixed_leg_type,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
###########################################################################
###########################################################################
###########################################################################
# BLACK'S MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("======= ZERO VOLATILITY ========")
model = Black(0.0000001)
testCases.print("Black Model", model._volatility)
valuePay = europeanSwaptionPay.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK PAY VALUE ZERO VOL:", valuePay)
valueRec = europeanSwaptionRec.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK REC VALUE ZERO VOL:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("======= 20%% BLACK VOLATILITY ========")
model = Black(0.20)
testCases.print("Black Model", model._volatility)
valuePay = europeanSwaptionPay.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BK MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("==================== BK MODEL =========================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======= 0% VOLATILITY EUROPEAN SWAPTION BK MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.000000001
a = 0.01
num_time_steps = 100
model = BKTree(sigma, a, num_time_steps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY EUROPEAN SWAPTION BK MODEL ========")
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.2
a = 0.01
model = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BDT MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======================= BDT MODEL =====================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("====== 0% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.00001
num_time_steps = 200
model = BDTTree(sigma, num_time_steps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("===== 20% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = BDTTree(sigma, num_time_steps)
testCases.banner("BDT MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
model = BDTTree(sigma, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.2
model = BDTTree(sigma, num_time_steps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = BDTTree(sigma, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = BDTTree(sigma, num_time_steps)
# print("BDT MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BDT MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======================= HW MODEL ======================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("====== 0% VOLATILITY EUROPEAN SWAPTION HW MODEL ======")
sigma = 0.0000001
a = 0.1
num_time_steps = 200
model = HWTree(sigma, a, num_time_steps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("===== 20% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.01
a = 0.01
model = HWTree(sigma, a, num_time_steps)
testCases.banner("HW MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE HW MODEL ========"
)
sigma = 0.000001
model = HWTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 100bp VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.01
model = HWTree(sigma, a, num_time_steps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = HWTree(sigma, a, num_time_steps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 100bps VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.01
a = 0.01
model = HWTree(sigma, a, num_time_steps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
def test_BondEmbeddedOptionMATLAB():
# https://fr.mathworks.com/help/fininst/optembndbybk.html
# I FIND THAT THE PRICE CONVERGES TO 102.365 WHICH IS CLOSE TO 102.382
# FOUND BY MATLAB ALTHOUGH THEY DO NOT EXAMINE THE ASYMPTOTIC PRICE
# WHICH MIGHT BE A BETTER MATCH - ALSO THEY DO NOT USE A REALISTIC VOL
valuation_date = Date(1, 1, 2007)
settlement_date = valuation_date
###########################################################################
fixed_leg_type = SwapTypes.PAY
dcType = DayCountTypes.THIRTY_E_360
fixedFreq = FrequencyTypes.ANNUAL
swap1 = IborSwap(settlement_date, "1Y", fixed_leg_type, 0.0350, fixedFreq, dcType)
swap2 = IborSwap(settlement_date, "2Y", fixed_leg_type, 0.0400, fixedFreq, dcType)
swap3 = IborSwap(settlement_date, "3Y", fixed_leg_type, 0.0450, fixedFreq, dcType)
swaps = [swap1, swap2, swap3]
discount_curve = IborSingleCurve(valuation_date, [], [], swaps)
###########################################################################
issue_date = Date(1, 1, 2005)
maturity_date = Date(1, 1, 2010)
coupon = 0.0525
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
call_dates = []
call_prices = []
put_dates = []
put_prices = []
putDate = Date(1, 1, 2008)
for _ in range(0, 24):
put_dates.append(putDate)
put_prices.append(100)
putDate = putDate.add_months(1)
testCases.header("BOND PRICE", "PRICE")
v = bond.clean_price_from_discount_curve(settlement_date, discount_curve)
testCases.print("Bond Pure Price:", v)
sigma = 0.01 # This volatility is very small for a BK process
a = 0.1
puttableBond = BondEmbeddedOption(issue_date, maturity_date, coupon,
freq_type, accrual_type,
call_dates, call_prices,
put_dates, put_prices)
testCases.header("TIME", "NumTimeSteps", "BondWithOption", "BondPure")
timeSteps = range(100, 200, 10) # 1000, 10)
values = []
for num_time_steps in timeSteps:
model = BKTree(sigma, a, num_time_steps)
start = time.time()
v = puttableBond.value(settlement_date, discount_curve, model)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v['bondwithoption'],
v['bondpure'])
values.append(v['bondwithoption'])
if plotGraphs:
plt.figure()
plt.plot(timeSteps, values)
valuation_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2012)
swapMaturityDate = Date(1, 1, 2017)
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
model1 = Black(0.00001)
model2 = BlackShifted(0.00001, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.00001, 0.00001)
model6 = BKTree(0.01, 0.01)
settlement_date = valuation_date.add_weekdays(2)
libor_curve = build_curve(valuation_date)
def test_pay():
libor_curve = build_curve(valuation_date)
swaptionType = SwapTypes.PAY
k = 0.02
swaption = IborSwaption(settlement_date, exercise_date, swapMaturityDate,
swaptionType, k, swapFixedFrequencyType,
swapFixedDayCountType)
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
def test_BondOption():
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
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)
tmat = (maturity_date - settlement_date) / gDaysInYear
times = np.linspace(0, tmat, 20)
dates = settlement_date.add_years(times)
dfs = np.exp(-0.05*times)
discount_curve = DiscountCurve(settlement_date, dates, dfs)
expiry_date = settlement_date.add_tenor("18m")
strike_price = 105.0
face = 100.0
###########################################################################
strikes = [80, 85, 90, 95, 100, 105, 110, 115, 120]
option_type = OptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.full_price_from_discount_curve(
settlement_date, discount_curve)
testCases.print("Fixed Income Price:", price)
num_time_steps = 20
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strike_price in strikes:
sigma = 0.20
a = 0.1
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a, num_time_steps)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("EUROPEAN CALL - BK", strike_price, v)
for strike_price in strikes:
sigma = 0.20
a = 0.05
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a, num_time_steps)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("EUROPEAN CALL - BK", strike_price, v)
###########################################################################
option_type = OptionTypes.AMERICAN_CALL
price = bond.full_price_from_discount_curve(
settlement_date, discount_curve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strike_price in strikes:
sigma = 0.01
a = 0.1
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("AMERICAN CALL - BK", strike_price, v)
for strike_price in strikes:
sigma = 0.20
a = 0.05
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("AMERICAN CALL - BK", strike_price, v)
###########################################################################
option_type = OptionTypes.EUROPEAN_PUT
price = bond.full_price_from_discount_curve(
settlement_date, discount_curve)
for strike_price in strikes:
sigma = 0.01
a = 0.1
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("EUROPEAN PUT - BK", strike_price, v)
for strike_price in strikes:
sigma = 0.20
a = 0.05
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("EUROPEAN PUT - BK", strike_price, v)
###########################################################################
option_type = OptionTypes.AMERICAN_PUT
price = bond.full_price_from_discount_curve(
settlement_date, discount_curve)
for strike_price in strikes:
sigma = 0.02
a = 0.1
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("AMERICAN PUT - BK", strike_price, v)
for strike_price in strikes:
sigma = 0.20
a = 0.05
bond_option = BondOption(
bond, expiry_date, strike_price, face, option_type)
model = BKTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print("AMERICAN PUT - BK", strike_price, v)
def test_BondOptionZEROVOLConvergence():
# Build discount curve
settlement_date = Date(1, 9, 2019)
rate = 0.05
discount_curve = DiscountCurveFlat(
settlement_date, rate, FrequencyTypes.ANNUAL)
# Bond details
issue_date = Date(1, 9, 2014)
maturity_date = Date(1, 9, 2025)
coupon = 0.06
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
# Option Details
expiry_date = Date(1, 12, 2021)
face = 100.0
dfExpiry = discount_curve.df(expiry_date)
fwdCleanValue = bond.clean_price_from_discount_curve(
expiry_date, discount_curve)
fwdFullValue = bond.full_price_from_discount_curve(
expiry_date, discount_curve)
# print("BOND FwdCleanBondPx", fwdCleanValue)
# print("BOND FwdFullBondPx", fwdFullValue)
# print("BOND Accrued:", bond._accrued_interest)
spotCleanValue = bond.clean_price_from_discount_curve(
settlement_date, discount_curve)
testCases.header("STRIKE", "STEPS",
"CALL_INT", "CALL_INT_PV", "CALL_EUR", "CALL_AMER",
"PUT_INT", "PUT_INT_PV", "PUT_EUR", "PUT_AMER")
num_time_steps = range(100, 1000, 100)
strike_prices = [90, 100, 110, 120]
for strike_price in strike_prices:
callIntrinsic = max(spotCleanValue - strike_price, 0)
putIntrinsic = max(strike_price - spotCleanValue, 0)
callIntrinsicPV = max(fwdCleanValue - strike_price, 0) * dfExpiry
putIntrinsicPV = max(strike_price - fwdCleanValue, 0) * dfExpiry
for num_steps in num_time_steps:
sigma = 0.0000001
a = 0.1
model = BKTree(sigma, a, num_steps)
option_type = OptionTypes.EUROPEAN_CALL
bond_option1 = BondOption(
bond, expiry_date, strike_price, face, option_type)
v1 = bond_option1.value(settlement_date, discount_curve, model)
option_type = OptionTypes.AMERICAN_CALL
bond_option2 = BondOption(
bond, expiry_date, strike_price, face, option_type)
v2 = bond_option2.value(settlement_date, discount_curve, model)
option_type = OptionTypes.EUROPEAN_PUT
bond_option3 = BondOption(
bond, expiry_date, strike_price, face, option_type)
v3 = bond_option3.value(settlement_date, discount_curve, model)
option_type = OptionTypes.AMERICAN_PUT
bond_option4 = BondOption(
bond, expiry_date, strike_price, face, option_type)
v4 = bond_option4.value(settlement_date, discount_curve, model)
testCases.print(strike_price, num_steps,
callIntrinsic, callIntrinsicPV, v1, v2,
putIntrinsic, putIntrinsicPV, v3, v4)
def test_BondEmbeddedOptionQUANTLIB():
# Based on example at the nice blog on Quantlib at
# http://gouthamanbalaraman.com/blog/callable-bond-quantlib-python.html
# I get a price of 68.97 for 1000 time steps which is higher than the
# 68.38 found in blog article. But this is for 40 grid points.
# Note also that a basis point vol of 0.120 is 12% which is VERY HIGH!
valuation_date = Date(16, 8, 2016)
settlement_date = valuation_date.add_weekdays(3)
###########################################################################
discount_curve = DiscountCurveFlat(valuation_date, 0.035,
FrequencyTypes.SEMI_ANNUAL)
###########################################################################
issue_date = Date(15, 9, 2010)
maturity_date = Date(15, 9, 2022)
coupon = 0.025
freq_type = FrequencyTypes.QUARTERLY
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
###########################################################################
# Set up the call and put times and prices
###########################################################################
nextCallDate = Date(15, 9, 2016)
call_dates = [nextCallDate]
call_prices = [100.0]
for _ in range(1, 24):
nextCallDate = nextCallDate.add_months(3)
call_dates.append(nextCallDate)
call_prices.append(100.0)
put_dates = []
put_prices = []
# the value used in blog of 12% bp vol is unrealistic
sigma = 0.12/0.035 # basis point volatility
a = 0.03
puttableBond = BondEmbeddedOption(issue_date, maturity_date, coupon,
freq_type, accrual_type,
call_dates, call_prices,
put_dates, put_prices)
testCases.header("BOND PRICE", "PRICE")
v = bond.clean_price_from_discount_curve(settlement_date, discount_curve)
testCases.print("Bond Pure Price:", v)
testCases.header("TIME", "NumTimeSteps", "BondWithOption", "BondPure")
timeSteps = range(100, 200, 20) # 1000, 10)
values = []
for num_time_steps in timeSteps:
model = BKTree(sigma, a, num_time_steps)
start = time.time()
v = puttableBond.value(settlement_date, discount_curve, model)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v['bondwithoption'],
v['bondpure'])
values.append(v['bondwithoption'])
if plotGraphs:
plt.figure()
plt.title("Puttable Bond Price Convergence")
plt.plot(timeSteps, values)