def test_BKExampleOne():
testCases.banner("=== HULL INITIAL EXAMPLE SECTION 28.7 ED 6 PG 668 ====")
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)
endDate = FinDate(1, 6, 2021)
sigma = 0.25
a = 0.22
numTimeSteps = 3
tmat = (endDate - startDate) / gDaysInYear
model = FinModelRatesBK(sigma, a, numTimeSteps)
model.buildTree(tmat, times, dfs)
# Agrees with Figure 28.10 - Not exact as we have dt not exactly 0.50
if numTimeSteps < 5:
testCases.header("LABEL", "VALUE")
testCases.print("QTREE", model._Q)
testCases.print("RTREE", model._rt)
printTree(model._rt)
testCases.print("PU AT LAST TIME", model._pu)
testCases.print("PDM AT LAST TIME", model._pm)
testCases.print("PD AT LAST TIME", model._pd)
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
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, frequencyType, 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)
curve = FinDiscountCurve(settlementDate, dates, dfs)
price = bond.cleanPriceFromDiscountCurve(settlementDate, curve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
sigma = 0.20
a = 0.05
numTimeSteps = 26
model = FinModelRatesBK(sigma, a, numTimeSteps)
model.buildTree(tmat, times, dfs)
exerciseType = FinOptionExerciseTypes.AMERICAN
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
exerciseType)
# Test convergence
numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
exerciseType = FinOptionExerciseTypes.AMERICAN
testCases.header("TIMESTEPS", "VALUE", "TIME")
treeVector = []
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesBK(sigma, a, numTimeSteps)
model.buildTree(tmat, times, dfs)
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
exerciseType)
end = time.time()
period = end - start
treeVector.append(v)
testCases.print(numTimeSteps, v, period)
# plt.plot(numStepsList, treeVector)
# Value in Hill converges to 0.699 with 100 time steps while I get 0.700
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("Q")
printTree(model._Q, 5)