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_FinShiftedSABR():
strikes = np.linspace(-0.006, 0.016, 10)
alpha = 0.013345
beta = 0.5
rho = 0.46698
nu = 0.49861
shift = 0.008
model = SABRShifted(alpha, beta, rho, nu, shift)
f = 0.0006384
T = 1.0
vols = model.black_vol(f, strikes, T)
if PLOT_GRAPHS:
plt.figure()
plt.plot(strikes, vols)
plt.title("SHIFTED SABR")
def test_FinShiftedSABRSimple():
strikes = np.linspace(0.01, 0.06, 10)
alpha = 0.060277
beta = 0.5
rho = 0.2097
nu = 0.75091
model1 = SABRShifted(alpha, beta, rho, nu, 0.0)
alpha = 0.058484
beta = 0.5
rho = 0.20568
nu = 0.79647
model2 = SABRShifted(alpha, beta, rho, nu, 0.0)
f = 0.0350
T = 1.0
vols1 = model1.black_vol(f, strikes, T)
vols2 = model2.black_vol(f, strikes, T)
if PLOT_GRAPHS:
plt.figure()
plt.plot(strikes, vols1)
plt.plot(strikes, vols2)
plt.title("Shifted SIMPLE SABR")
def test_IborSwaptionQLExample():
valuation_date = Date(4, 3, 2014)
settlement_date = Date(4, 3, 2014)
depoDCCType = DayCountTypes.THIRTY_E_360_ISDA
depos = []
depo = IborDeposit(settlement_date, "1W", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "1M", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "3M", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "6M", 0.0023, depoDCCType)
depos.append(depo)
# No convexity correction provided so I omit interest rate futures
swaps = []
accType = DayCountTypes.ACT_365F
fixedFreqType = FrequencyTypes.SEMI_ANNUAL
fixed_leg_type = SwapTypes.PAY
swap = IborSwap(settlement_date, "3Y", fixed_leg_type, 0.00790,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "4Y", fixed_leg_type, 0.01200,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "5Y", fixed_leg_type, 0.01570,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "6Y", fixed_leg_type, 0.01865,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "7Y", fixed_leg_type, 0.02160,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "8Y", fixed_leg_type, 0.02350,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "9Y", fixed_leg_type, 0.02540,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "10Y", fixed_leg_type, 0.0273,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "15Y", fixed_leg_type, 0.0297,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "20Y", fixed_leg_type, 0.0316,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "25Y", fixed_leg_type, 0.0335,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "30Y", fixed_leg_type, 0.0354,
fixedFreqType, accType)
swaps.append(swap)
libor_curve = IborSingleCurve(valuation_date, depos, [], swaps,
InterpTypes.LINEAR_ZERO_RATES)
exercise_date = settlement_date.add_tenor("5Y")
swapMaturityDate = exercise_date.add_tenor("5Y")
swapFixedCoupon = 0.040852
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.THIRTY_E_360_ISDA
swapFloatFrequencyType = FrequencyTypes.QUARTERLY
swapFloatDayCountType = DayCountTypes.ACT_360
swapNotional = 1000000
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, swapMaturityDate,
swaptionType, swapFixedCoupon,
swapFixedFrequencyType, swapFixedDayCountType,
swapNotional, swapFloatFrequencyType,
swapFloatDayCountType)
testCases.header("MODEL", "VALUE")
model = Black(0.1533)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = BlackShifted(0.1533, -0.008)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = SABR(0.132, 0.5, 0.5, 0.5)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = SABRShifted(0.352, 0.5, 0.15, 0.15, -0.005)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = HWTree(0.010000000, 0.00000000001)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
def test_FinIborCapFloor():
todayDate = Date(20, 6, 2019)
valuation_date = todayDate
start_date = todayDate.add_weekdays(2)
maturity_date = start_date.add_tenor("1Y")
libor_curve = test_ibor_depositsAndSwaps(todayDate)
# The capfloor has begun
# lastFixing = 0.028
##########################################################################
# COMPARISON OF MODELS
##########################################################################
strikes = np.linspace(0.02, 0.08, 5)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BACH")
model1 = Black(0.20)
model2 = BlackShifted(0.25, 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(0.30, 0.01)
model6 = Bachelier(0.01)
for k in strikes:
capFloorType = FinCapFloorTypes.CAP
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)
testCases.print("CAP", k, cvalue1, cvalue2,
cvalue3, cvalue4, cvalue5, cvalue6)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BACH")
for k in strikes:
capFloorType = FinCapFloorTypes.FLOOR
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
fvalue1 = capfloor.value(valuation_date, libor_curve, model1)
fvalue2 = capfloor.value(valuation_date, libor_curve, model2)
fvalue3 = capfloor.value(valuation_date, libor_curve, model3)
fvalue4 = capfloor.value(valuation_date, libor_curve, model4)
fvalue5 = capfloor.value(valuation_date, libor_curve, model5)
fvalue6 = capfloor.value(valuation_date, libor_curve, model6)
testCases.print("FLR", k, fvalue1, fvalue2,
fvalue3, fvalue4, fvalue5, fvalue6)
###############################################################################
# PUT CALL CHECK
###############################################################################
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR SHFTD", "HW", "BACH")
for k in strikes:
capFloorType = FinCapFloorTypes.CAP
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)
capFloorType = FinCapFloorTypes.FLOOR
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
fvalue1 = capfloor.value(valuation_date, libor_curve, model1)
fvalue2 = capfloor.value(valuation_date, libor_curve, model2)
fvalue3 = capfloor.value(valuation_date, libor_curve, model3)
fvalue4 = capfloor.value(valuation_date, libor_curve, model4)
fvalue5 = capfloor.value(valuation_date, libor_curve, model5)
fvalue6 = capfloor.value(valuation_date, libor_curve, model6)
pcvalue1 = cvalue1 - fvalue1
pcvalue2 = cvalue2 - fvalue2
pcvalue3 = cvalue3 - fvalue3
pcvalue4 = cvalue4 - fvalue4
pcvalue5 = cvalue5 - fvalue5
pcvalue6 = cvalue6 - fvalue6
testCases.print("PUT_CALL", k, pcvalue1, pcvalue2, pcvalue3,
pcvalue4, pcvalue5, pcvalue6)
def test_ShiftedSABR():
testCases.header("TEST", "CALIBRATION ERROR")
alpha = 0.0
beta = 0.5
rho = -0.09
nu = 0.1
shift = 0.02
strikeVol = 0.1
f = 0.043
k = 0.050
r = 0.03
texp = 2.0
call_optionType = FinOptionTypes.EUROPEAN_CALL
put_optionType = FinOptionTypes.EUROPEAN_PUT
df = np.exp(-r * texp)
# SABR equivalent to lognormal (Black) model (i.e. beta = 1, rho = 0, nu = 0, shift = 0)
modelSABR_01 = SABRShifted(0.0, 1.0, 0.0, 0.0, 0.0)
modelSABR_01.set_alpha_from_black_vol(strikeVol, f, k, texp)
impliedLognormalVol = modelSABR_01.black_vol(f, k, texp)
impliedATMLognormalVol = modelSABR_01.black_vol(k, k, texp)
impliedLognormalSmile = impliedLognormalVol - impliedATMLognormalVol
assert impliedLognormalSmile == 0.0, "In lognormal model, smile should be flat"
calibrationError = round(strikeVol - impliedLognormalVol, 12)
testCases.print("LOGNORMAL CASE", calibrationError)
# Volatility: pure SABR dynamics
modelSABR_02 = SABRShifted(alpha, beta, rho, nu, shift)
modelSABR_02.set_alpha_from_black_vol(strikeVol, f, k, texp)
impliedLognormalVol = modelSABR_02.black_vol(f, k, texp)
impliedATMLognormalVol = modelSABR_02.black_vol(k, k, texp)
impliedLognormalSmile = impliedLognormalVol - impliedATMLognormalVol
calibrationError = round(strikeVol - impliedLognormalVol, 12)
testCases.print("SABR CASE", calibrationError)
# Valuation: pure SABR dynamics
valueCall = modelSABR_02.value(f, k, texp, df, call_optionType)
valuePut = modelSABR_02.value(f, k, texp, df, put_optionType)
assert round((valueCall - valuePut), 12) == round(df*(f - k), 12), \
"The method called 'value()' doesn't comply with Call-Put parity"
libor_curve = IborSingleCurve(valuation_date, depos, fras, swaps)
return libor_curve
todayDate = Date(20, 6, 2019)
valuation_date = todayDate
start_date = todayDate.add_weekdays(2)
maturity_date = start_date.add_tenor("1Y")
libor_curve = build_curve(todayDate)
model1 = Black(0.20)
model2 = BlackShifted(0.25, 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(0.30, 0.01)
model6 = Bachelier(0.01)
def test_cap():
capFloorType = FinCapFloorTypes.CAP
k = 0.02
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)