def test_FinInterpolatedForwards():
import matplotlib.pyplot as plt
tValues = np.array([0.0, 3.0, 5.0, 10.0])
rValues = np.array([0.04, 0.07, 0.08, 0.09])
dfValues = np.exp(-tValues*rValues)
tInterpValues = np.linspace(0.0, 12.0, 200)
print(tValues)
print(rValues)
print(dfValues)
curveDate = FinDate(2019,1,3)
for method in FinInterpMethods:
discountCurve = FinDiscountCurve(curveDate, tValues, dfValues, method)
dfInterpValues = discountCurve.df(tInterpValues)
fwdInterpValues = discountCurve.fwd(tInterpValues)
zeroInterpValues = discountCurve.zeroRate(tInterpValues)
if PLOT_GRAPHS:
plt.figure(figsize=(8, 6))
plt.plot(tValues, dfValues, 'o', color='g', label="DFS:")
plt.plot(tInterpValues, dfInterpValues, color='r', label="DF:" + str(method))
plt.legend()
plt.figure(figsize=(8, 6))
plt.plot(tInterpValues, fwdInterpValues, color='r', label="FWD:" + str(method))
plt.plot(tInterpValues, zeroInterpValues, color='b', label="ZERO:" + str(method))
plt.plot(tValues, rValues, 'o', color='g', label="ZERO RATES")
plt.legend()
def test_FinDiscountCurve():
startDate = FinDate(2018, 1, 1)
times = np.linspace(0, 10.0, 10)
rate = 0.05
values = np.exp(-rate * times)
curve = FinDiscountCurve(startDate, times, values,
FinInterpMethods.FLAT_FORWARDS)
testCases.header("T", "DF")
for t in np.linspace(0, 10, 21):
df = curve.df(t)
testCases.print(t, df)
def test_CDSFastApproximation():
valueDate = FinDate(2018, 6, 20)
# I build a discount curve that requires no bootstrap
times = np.linspace(0, 10.0, 11)
r = 0.05
discountFactors = np.power((1.0 + r), -times)
dates = valueDate.addYears(times)
liborCurve = FinDiscountCurve(valueDate,
dates,
discountFactors,
FinInterpTypes.FLAT_FWD_RATES)
##########################################################################
maturityDate = valueDate.nextCDSDate(120)
t = (maturityDate - valueDate) / 365.242
z = liborCurve.df(maturityDate)
r = -np.log(z) / t
recoveryRate = 0.40
contractCoupon = 0.010
testCases.header("MKT_SPD", "EXACT_VALUE", "APPROX_VALUE", "DIFF(%NOT)")
for mktCoupon in np.linspace(0.000, 0.05, 21):
cdsContracts = []
cdsMkt = FinCDS(valueDate, maturityDate, mktCoupon, ONE_MILLION)
cdsContracts.append(cdsMkt)
issuerCurve = FinCDSCurve(valueDate,
cdsContracts,
liborCurve,
recoveryRate)
cdsContract = FinCDS(valueDate, maturityDate, contractCoupon)
v_exact = cdsContract.value(
valueDate, issuerCurve, recoveryRate)['full_pv']
v_approx = cdsContract.valueFastApprox(
valueDate, r, mktCoupon, recoveryRate)[0]
pctdiff = (v_exact - v_approx) / ONE_MILLION * 100.0
testCases.print(mktCoupon * 10000, v_exact, v_approx, pctdiff)
def test_BlackKarasinskiExampleTwo():
# 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
settlementDate = FinDate(1, 12, 2019)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
texp = (expiryDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
price = bond.fullPriceFromDiscountCurve(settlementDate, curve)
print("Fixed Income Price:", price)
sigma = 0.20
a = 0.05
# Test convergence
numStepsList = [100] #,101,200,300,400,500,600,700,800,900,1000]
isAmerican = True
treeVector = []
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesBlackKarasinski(a, sigma)
model.buildTree(tmat, int(numTimeSteps), times, dfs)
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
isAmerican)
end = time.time()
period = end - start
treeVector.append(v[0])
print(numTimeSteps, v, period)
def test_IssuerCurveBuild():
''' Test issuer curve build with simple libor curve to isolate cds
curve building time cost. '''
valuationDate = FinDate(20, 6, 2018)
times = np.linspace(0.0, 10.0, 11)
r = 0.05
discountFactors = np.power((1.0 + r), -times)
dates = valuationDate.addYears(times)
liborCurve = FinDiscountCurve(valuationDate,
dates,
discountFactors,
FinInterpTypes.FLAT_FWD_RATES)
recoveryRate = 0.40
cdsContracts = []
cdsCoupon = 0.005 # 50 bps
maturityDate = valuationDate.addMonths(12)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0055
maturityDate = valuationDate.addMonths(24)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0060
maturityDate = valuationDate.addMonths(36)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0065
maturityDate = valuationDate.addMonths(60)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0070
maturityDate = valuationDate.addMonths(84)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0073
maturityDate = valuationDate.addMonths(120)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
issuerCurve = FinCDSCurve(valuationDate,
cdsContracts,
liborCurve,
recoveryRate)
return cdsContracts, issuerCurve
def test_FinInterpolatedForwards():
import matplotlib.pyplot as plt
tValues = np.array([0.0, 3.0, 5.0, 10.0])
rValues = np.array([0.04, 0.07, 0.08, 0.09])
dfValues = np.exp(-tValues * rValues)
tInterpValues = np.linspace(0.0, 12.0, 49)
curveDate = FinDate(1, 1, 2019)
tDates = curveDate.addYears(tValues)
tInterpDates = curveDate.addYears(tInterpValues)
for interpType in FinInterpTypes:
discountCurve = FinDiscountCurve(curveDate, tDates, dfValues,
interpType)
dfInterpValues = discountCurve.df(tInterpDates)
fwdInterpValues = discountCurve.fwd(tInterpDates)
zeroInterpValues = discountCurve.zeroRate(tInterpDates)
if PLOT_GRAPHS:
plt.figure(figsize=(8, 6))
plt.plot(tValues, dfValues, 'o', color='g', label="DFS:")
plt.plot(tInterpValues,
dfInterpValues,
color='r',
label="DF:" + str(interpType))
plt.legend()
plt.figure(figsize=(8, 6))
plt.plot(tInterpValues,
fwdInterpValues,
color='r',
label="FWD:" + str(interpType))
plt.plot(tInterpValues,
zeroInterpValues,
color='b',
label="ZERO:" + str(interpType))
plt.plot(tValues, rValues, 'o', color='g', label="ZERO RATES")
plt.legend()
def test_dp_example():
# http://www.derivativepricing.com/blogpage.asp?id=8
startDate = FinDate(14, 11, 2011)
endDate = FinDate(14, 11, 2016)
fixedFreqType = FinFrequencyTypes.SEMI_ANNUAL
swapCalendarType = FinCalendarTypes.TARGET
busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING
dateGenRuleType = FinDateGenRuleTypes.BACKWARD
fixedDayCountType = FinDayCountTypes.THIRTY_E_360_ISDA
swapType = FinLiborSwapTypes.PAYER
fixedCoupon = 0.0124
notional = ONE_MILLION
swap = FinLiborSwap(startDate,
endDate,
swapType,
fixedCoupon=fixedCoupon,
fixedFreqType=fixedFreqType,
fixedDayCountType=fixedDayCountType,
floatFreqType=FinFrequencyTypes.SEMI_ANNUAL,
floatDayCountType=FinDayCountTypes.ACT_360,
notional=notional,
calendarType=swapCalendarType,
busDayAdjustType=busDayAdjustType,
dateGenRuleType=dateGenRuleType)
# swap.printFixedLegFlows()
dts = [FinDate(14, 11, 2011), FinDate(14, 5, 2012), FinDate(14, 11, 2012),
FinDate(14, 5, 2013), FinDate(14, 11, 2013), FinDate(14, 5, 2014),
FinDate(14, 11, 2014), FinDate(14, 5, 2015), FinDate(16, 11, 2015),
FinDate(16, 5, 2016), FinDate(14, 11, 2016)]
dfs = [0.9999843, 0.9966889, 0.9942107, 0.9911884, 0.9880738, 0.9836490,
0.9786276, 0.9710461, 0.9621778, 0.9514315, 0.9394919]
valuationDate = startDate
curve = FinDiscountCurve(valuationDate, dts, np.array(dfs),
FinInterpTypes.FLAT_FORWARDS)
v = swap.value(valuationDate, curve, curve)
# swap.printFixedLegPV()
# swap.printFloatLegPV()
# This is essentially zero
testCases.header("LABEL", "VALUE")
testCases.print("Swap Value on a Notional of $1M:", v)
def test_CurveBuild():
valuationDate = FinDate(2018, 6, 20)
times = np.linspace(0.0, 10.0, 10)
r = 0.05
discountFactors = np.power((1.0 + r), -times)
liborCurve = FinDiscountCurve(valuationDate, times, discountFactors,
FinInterpMethods.FLAT_FORWARDS)
recoveryRate = 0.40
cdsContracts = []
cdsCoupon = 0.005 # 50 bps
maturityDate = valuationDate.addMonths(12)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0055
maturityDate = valuationDate.addMonths(24)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0060
maturityDate = valuationDate.addMonths(36)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0065
maturityDate = valuationDate.addMonths(60)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0070
maturityDate = valuationDate.addMonths(84)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
cdsCoupon = 0.0073
maturityDate = valuationDate.addMonths(120)
cds = FinCDS(valuationDate, maturityDate, cdsCoupon)
cdsContracts.append(cds)
issuerCurve = FinCDSCurve(valuationDate, cdsContracts, liborCurve,
recoveryRate)
return cdsContracts, issuerCurve
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
discountCurve = FinDiscountCurve(settlementDate, times, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
optionType = FinBondOptionTypes.AMERICAN_CALL
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
print("Fixed Income Price:", price)
for strikePrice in [90, 95, 100, 105, 110]:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHullWhite(a, sigma)
v = bondOption.value(settlementDate, discountCurve, model)
print("HW", strikePrice, v)
for strikePrice in [90, 95, 100, 105, 110]:
sigma = 0.20
a = 0.05
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBlackKarasinski(a, sigma)
v = bondOption.value(settlementDate, discountCurve, model)
print("BK", strikePrice, v)
def test_BlackKarasinskiExampleOne():
# HULL BOOK INITIAL EXAMPLE SECTION 28.7 HW EDITION 6
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)
startDate = FinDate(1, 12, 2019)
curve = FinDiscountCurve(startDate, times, dfs)
endDate = FinDate(1, 12, 2022)
sigma = 0.25
a = 0.22
numTimeSteps = 6
tmat = (endDate - startDate) / gDaysInYear
model = FinModelRatesBlackKarasinski(a, sigma)
model.buildTree(tmat, numTimeSteps, times, dfs)
printTree(model._Q)
print("")
printTree(model._rt)
print("")
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()
settlementDate = FinDate(1, 1, 2020)
times = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
dates = settlementDate.addYears(times)
rate = 0.06
dfs = 1.0 / (1.0 + rate / 2.0)**(2.0 * times)
curve = FinDiscountCurve(settlementDate, dates, dfs)
coupon = 0.06
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
strikePrice = 100.0
face = 100.0
# Andersen paper
numTimeSteps = 200
testCases.header("ExerciseType", "Sigma", "NumSteps", "Texp", "Tmat",
"V_Fixed", "V_pay", "V_rec")
for exerciseType in [FinExerciseTypes.EUROPEAN, FinExerciseTypes.BERMUDAN]:
for maturityYears in [4.0, 5.0, 10.0, 20.0]:
maturityDate = settlementDate.addYears(maturityYears)
issueDate = FinDate(maturityDate._d, maturityDate._m, 2000)
if maturityYears == 4.0 or maturityYears == 5.0:
sigma = 0.2012
elif maturityYears == 10.0:
sigma = 0.1522
elif maturityYears == 20.0:
sigma = 0.1035
for expiryYears in range(
int(maturityYears / 2) - 1, int(maturityYears)):
expiryDate = settlementDate.addYears(expiryYears)
tmat = (maturityDate - settlementDate) / gDaysInYear
texp = (expiryDate - settlementDate) / gDaysInYear
bond = FinBond(issueDate, maturityDate, coupon, freqType,
accrualType)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates:
if flowDate > expiryDate:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
price = bond.cleanPriceFromDiscountCurve(settlementDate, curve)
model = FinModelRatesBDT(sigma, numTimeSteps)
model.buildTree(tmat, times, dfs)
v = model.bermudanSwaption(texp, tmat, strikePrice, face,
couponTimes, couponFlows,
exerciseType)
testCases.print("%s" % exerciseType, "%9.5f" % sigma,
"%9.5f" % numTimeSteps, "%9.5f" % expiryYears,
"%9.5f" % maturityYears, "%9.5f" % price,
"%9.2f" % (v['pay'] * 100.0),
"%9.2f" % (v['rec'] * 100.0))
def test_BDTExampleTwo():
# Valuation of a European option on a coupon bearing bond
# This follows example in Fig 28.11 of John Hull's book (6th Edition)
# but does not have the exact same dt so there are some differences
testCases.banner("===================== FIG 28.11 HULL BOOK =============")
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2015)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
numFlows = len(bond._flowDates)
for i in range(1, numFlows):
pcd = bond._flowDates[i - 1]
ncd = bond._flowDates[i]
if pcd < settlementDate and ncd > settlementDate:
flowTime = (pcd - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
for flowDate in bond._flowDates:
if flowDate > settlementDate:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
texp = (expiryDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 11)
dates = settlementDate.addYears(times)
dfs = np.exp(-0.05 * times)
testCases.header("LABEL", "VALUES")
testCases.print("TIMES:", times)
curve = FinDiscountCurve(settlementDate, dates, dfs)
price = bond.cleanPriceFromDiscountCurve(settlementDate, curve)
testCases.print("Fixed Income Price:", price)
sigma = 0.20
# Test convergence
numStepsList = [5] #[100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
exerciseType = FinExerciseTypes.AMERICAN
testCases.header("Values")
treeVector = []
for numTimeSteps in numStepsList:
model = FinModelRatesBDT(sigma, numTimeSteps)
model.buildTree(tmat, times, dfs)
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
exerciseType)
testCases.print(v)
treeVector.append(v['call'])
if PLOT_GRAPHS:
plt.plot(numStepsList, treeVector)
# The value in Hull converges to 0.699 with 100 time steps while I get 0.70
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("Q")
printTree(model._Q, 5)
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dates = settlementDate.addYears(times)
dfs = np.exp(-0.05 * times)
discountCurve = FinDiscountCurve(settlementDate, dates, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
###########################################################################
strikes = [80, 90, 100, 110, 120]
optionType = FinOptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.print("Fixed Income Price:", price)
numTimeSteps = 100
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN CALL - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN CALL - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_CALL
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN CALL - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN CALL - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.EUROPEAN_PUT
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.01
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN PUT - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN PUT - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_PUT
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.02
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN PUT - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN PUT - BK", strikePrice, v)
def test_FinDiscountCurve():
# Create a curve from times and discount factors
startDate = FinDate(1, 1, 2018)
years = np.linspace(0, 10, 6)
rate = 0.05 + 0.005*years - 0.0003*years*years
dfs = np.exp(-rate * years)
dates = startDate.addYears(years)
curve = FinDiscountCurve(startDate, dates, dfs, FinInterpTypes.FLAT_FORWARDS)
testCases.header("T", "DF", "ZERORATE", "CC_FWD", "MM_FWD", "SURVPROB")
plotYears = np.linspace(0, 12, 12*12+1)
plotDates = startDate.addYears(plotYears)
# Examine dependency of curve on compounding rate
zeroRates_A = curve.zeroRate(plotDates, FinFrequencyTypes.ANNUAL)
zeroRates_S = curve.zeroRate(plotDates, FinFrequencyTypes.SEMI_ANNUAL)
zeroRates_Q = curve.zeroRate(plotDates, FinFrequencyTypes.QUARTERLY)
zeroRates_M = curve.zeroRate(plotDates, FinFrequencyTypes.MONTHLY)
zeroRates_C = curve.zeroRate(plotDates, FinFrequencyTypes.CONTINUOUS)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(plotYears, scale(zeroRates_A, 100), label='A')
plt.plot(plotYears, scale(zeroRates_S, 100), label='S')
plt.plot(plotYears, scale(zeroRates_Q, 100), label='Q')
plt.plot(plotYears, scale(zeroRates_M, 100), label='M')
plt.plot(plotYears, scale(zeroRates_C, 100), label='C')
plt.ylim((5, 8))
plt.title('Discount Curves')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)
# Examine dependency of fwd curve on the interpolation scheme
for interp in FinInterpTypes:
curve = FinDiscountCurve(startDate, dates, dfs, interp)
fwdRates = curve.fwd(plotDates)
zeroRates = curve.zeroRate(plotDates, FinFrequencyTypes.ANNUAL)
parRates = curve.swapRate(startDate, plotDates, FinFrequencyTypes.ANNUAL)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(plotYears, scale(fwdRates, 100), label='FWD RATES')
plt.plot(plotYears, scale(zeroRates, 100), label='ZERO RATES')
plt.plot(plotYears, scale(parRates, 100), label='PAR RATES')
plt.ylim((3.0, 8.5))
plt.title('Forward Curves using ' + str(interp))
plt.xlabel('Time (years)')
plt.ylabel('Fwd Rate (%)')
plt.legend(loc='lower right', frameon=False)
def test_HullWhiteCallableBond():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates[1:]:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
###########################################################################
# Set up the call and put times and prices
###########################################################################
callDates = []
callPrices = []
callPx = 120.0
callDates.append(settlementDate.addTenor("5Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("6Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("7Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("8Y"))
callPrices.append(callPx)
callTimes = []
for dt in callDates:
t = (dt - settlementDate) / gDaysInYear
callTimes.append(t)
putDates = []
putPrices = []
putPx = 98.0
putDates.append(settlementDate.addTenor("5Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("6Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("7Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("8Y"))
putPrices.append(putPx)
putTimes = []
for dt in putDates:
t = (dt - settlementDate) / gDaysInYear
putTimes.append(t)
###########################################################################
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
###########################################################################
v1 = bond.fullPriceFromDiscountCurve(settlementDate, curve)
sigma = 0.02 # basis point volatility
a = 0.1
# Test convergence
numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
tmat = (maturityDate - settlementDate) / gDaysInYear
print("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHullWhite(a, sigma)
model.buildTree(tmat, numTimeSteps, times, dfs)
v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows,
callTimes, callPrices, putTimes,
putPrices)
end = time.time()
period = end - start
print(numTimeSteps, v1, v2, period)
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("BOND")
printTree(model._bondValues, 5)
print("OPTION")
printTree(model._optionValues, 5)
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
times = np.linspace(0, 10.0, 21)
dfs = np.exp(-0.05 * times)
dates = settlementDate.addYears(times)
discountCurve = FinDiscountCurve(settlementDate, dates, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
###########################################################################
strikes = [80, 85, 90, 95, 100, 105, 110, 115, 120]
optionType = FinOptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.print("Fixed Income Price:", price)
numTimeSteps = 100
testCases.banner("HW EUROPEAN CALL")
testCases.header("STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_CALL
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.banner("HW AMERICAN CALL")
testCases.header("STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.EUROPEAN_PUT
testCases.banner("HW EUROPEAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_PUT
testCases.banner("HW AMERICAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.02
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
def test_FinDiscountCurves():
# Create a curve from times and discount factors
valuationDate = FinDate(1, 1, 2018)
years = [1.0, 2.0, 3.0, 4.0, 5.0]
dates = valuationDate.addYears(years)
years2 = []
for dt in dates:
y = (dt - valuationDate) / gDaysInYear
years2.append(y)
rates = np.array([0.05, 0.06, 0.065, 0.07, 0.075])
discountFactors = np.exp(-np.array(rates) * np.array(years2))
curvesList = []
finDiscountCurve = FinDiscountCurve(valuationDate, dates, discountFactors,
FinInterpTypes.FLAT_FORWARDS)
curvesList.append(finDiscountCurve)
finDiscountCurveFlat = FinDiscountCurveFlat(valuationDate, 0.05)
curvesList.append(finDiscountCurveFlat)
finDiscountCurveNS = FinDiscountCurveNS(valuationDate, 0.0305, -0.01, 0.08,
10.0)
curvesList.append(finDiscountCurveNS)
finDiscountCurveNSS = FinDiscountCurveNSS(valuationDate, 0.035, -0.02,
0.09, 0.1, 1.0, 2.0)
curvesList.append(finDiscountCurveNSS)
finDiscountCurvePoly = FinDiscountCurvePoly(valuationDate,
[0.05, 0.002, -0.00005])
curvesList.append(finDiscountCurvePoly)
finDiscountCurvePWF = FinDiscountCurvePWF(valuationDate, dates, rates)
curvesList.append(finDiscountCurvePWF)
finDiscountCurvePWL = FinDiscountCurvePWL(valuationDate, dates, rates)
curvesList.append(finDiscountCurvePWL)
finDiscountCurveZeros = FinDiscountCurveZeros(valuationDate, dates, rates)
curvesList.append(finDiscountCurveZeros)
curveNames = []
for curve in curvesList:
curveNames.append(type(curve).__name__)
testCases.banner("SINGLE CALLS NO VECTORS")
testCases.header("CURVE", "DATE", "ZERO", "DF", "CCFWD", "MMFWD", "SWAP")
years = np.linspace(1, 10, 10)
fwdMaturityDates = valuationDate.addYears(years)
testCases.banner("######################################################")
testCases.banner("SINGLE CALLS")
testCases.banner("######################################################")
for name, curve in zip(curveNames, curvesList):
for fwdMaturityDate in fwdMaturityDates:
tenor = "3M"
zeroRate = curve.zeroRate(fwdMaturityDate)
fwd = curve.fwd(fwdMaturityDate)
fwdRate = curve.fwdRate(fwdMaturityDate, tenor)
swapRate = curve.swapRate(valuationDate, fwdMaturityDate)
df = curve.df(fwdMaturityDate)
testCases.print("%-20s" % name, "%-12s" % fwdMaturityDate,
"%7.6f" % (zeroRate), "%8.7f" % (df),
"%7.6f" % (fwd), "%7.6f" % (fwdRate),
"%7.6f" % (swapRate))
# Examine vectorisation
testCases.banner("######################################################")
testCases.banner("VECTORISATIONS")
testCases.banner("######################################################")
for name, curve in zip(curveNames, curvesList):
tenor = "3M"
zeroRate = curve.zeroRate(fwdMaturityDates)
fwd = curve.fwd(fwdMaturityDates)
fwdRate = curve.fwdRate(fwdMaturityDates, tenor)
swapRate = curve.swapRate(valuationDate, fwdMaturityDates)
df = curve.df(fwdMaturityDates)
for i in range(0, len(fwdMaturityDates)):
testCases.print("%-20s" % name, "%-12s" % fwdMaturityDate,
"%7.6f" % (zeroRate[i]), "%8.7f" % (df[i]),
"%7.6f" % (fwd[i]), "%7.6f" % (fwdRate[i]),
"%7.6f" % (swapRate[i]))
if PLOT_GRAPHS:
years = np.linspace(0, 10, 121)
years2 = years + 1.0
fwdDates = valuationDate.addYears(years)
fwdDates2 = valuationDate.addYears(years2)
plt.figure()
for name, curve in zip(curveNames, curvesList):
zeroRates = curve.zeroRate(fwdDates)
plt.plot(years, zeroRates, label=name)
plt.legend()
plt.title("Zero Rates")
plt.figure()
for name, curve in zip(curveNames, curvesList):
fwdRates = curve.fwd(fwdDates)
plt.plot(years, fwdRates, label=name)
plt.legend()
plt.title("CC Fwd Rates")
plt.figure()
for name, curve in zip(curveNames, curvesList):
fwdRates = curve.fwdRate(fwdDates, fwdDates2)
plt.plot(years, fwdRates, label=name)
plt.legend()
plt.title("CC Fwd Rates")
plt.figure()
for name, curve in zip(curveNames, curvesList):
dfs = curve.df(fwdDates)
plt.plot(years, dfs, label=name)
plt.legend()
plt.title("Discount Factors")
def test_HullWhiteBondOption():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates[1:]:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
price = bond.fullPriceFromDiscountCurve(settlementDate, curve)
print("Spot Bond Price:", price)
price = bond.fullPriceFromDiscountCurve(expiryDate, curve)
print("Fwd Bond Price:", price)
sigma = 0.01
a = 0.1
# Test convergence
numStepsList = [100, 200, 300, 400, 500]
texp = (expiryDate - settlementDate) / gDaysInYear
print("NUMSTEPS", "FAST TREE", "FULLTREE", "TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHullWhite(a, sigma)
model.buildTree(texp, numTimeSteps, times, dfs)
americanExercise = False
v1 = model.americanBondOption_Tree(texp, strikePrice, face,
couponTimes, couponFlows,
americanExercise)
v2 = model.europeanBondOption_Tree(texp, strikePrice, face,
couponTimes, couponFlows)
end = time.time()
period = end - start
print(numTimeSteps, v1, v2, period)
# plt.plot(numStepsList, treeVector)
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("BOND")
printTree(model._bondValues, 5)
print("OPTION")
printTree(model._optionValues, 5)
v = model.europeanBondOption_Jamshidian(texp, strikePrice, face,
couponTimes, couponFlows, times,
dfs)
print("EUROPEAN BOND JAMSHIDIAN DECOMP", v)