def test_BDTExampleOne():
# HULL BOOK NOTES
# http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote23.pdf
valuationDate = FinDate(1, 1, 2020)
years = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
zeroDates = valuationDate.addYears(years)
zeroRates = [0.00, 0.10, 0.11, 0.12, 0.125, 0.13]
testCases.header("DATES")
testCases.print(zeroDates)
testCases.header("RATES")
testCases.print(zeroRates)
curve = FinDiscountCurveZeros(valuationDate, zeroDates, zeroRates,
FinFrequencyTypes.ANNUAL)
yieldVol = 0.16
numTimeSteps = 5
tmat = years[-1]
dfs = curve.df(zeroDates)
testCases.print("DFS")
testCases.print(dfs)
years = np.array(years)
dfs = np.array(dfs)
model = FinModelRatesBDT(yieldVol, numTimeSteps)
model.buildTree(tmat, years, dfs)
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)
