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_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_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_BondOptionDerivaGem():
# See https://github.com/domokane/FinancePy/issues/98
settlement_date = Date(1, 12, 2019)
rate = 0.05
dcType = DayCountTypes.THIRTY_360_BOND
fixedFreq = FrequencyTypes.SEMI_ANNUAL
discount_curve = DiscountCurveFlat(settlement_date, rate, fixedFreq,
dcType)
issue_date = Date(1, 12, 2018)
expiry_date = settlement_date.add_tenor("18m")
maturity_date = settlement_date.add_tenor("10Y")
coupon = 0.05
freqType = FrequencyTypes.SEMI_ANNUAL
accrualType = DayCountTypes.THIRTY_360_BOND
bond = Bond(issue_date, maturity_date, coupon, freqType, accrualType)
strike_price = 100.0
face = 100.0
europeanCallBondOption = BondOption(bond, expiry_date, strike_price, face,
OptionTypes.EUROPEAN_CALL)
cp = bond.clean_price_from_discount_curve(expiry_date, discount_curve)
fp = bond.full_price_from_discount_curve(expiry_date, discount_curve)
# print("Fixed Income Clean Price: %9.3f"% cp)
# print("Fixed Income Full Price: %9.3f"% fp)
num_steps = 500
sigma = 0.0125
a = 0.1
modelHW = HWTree(sigma, a, num_steps)
ec = europeanCallBondOption.value(settlement_date, discount_curve, modelHW)
###########################################################################
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
numFlows = len(bond._flow_dates)
for i in range(0, numFlows):
pcd = bond._flow_dates[i - 1]
ncd = bond._flow_dates[i]
if ncd > settlement_date:
if len(couponTimes) == 0:
flowTime = (pcd - settlement_date) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
flowTime = (ncd - settlement_date) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
y = 0.05
times = np.linspace(0, 10, 21)
dfs = np.power(1 + y / 2, -times * 2)
sigma = 0.0125
a = 0.1
model = HWTree(sigma, a, None)
# Test convergence
texp = (expiry_date - settlement_date) / gDaysInYear
tmat = (maturity_date - settlement_date) / gDaysInYear
# Jamshidian approach
vjam = model.european_bond_option_jamshidian(texp, strike_price, face,
couponTimes, couponFlows,
times, dfs)
# print("Jamshidian:", vjam)
model._num_time_steps = 100
model.build_tree(tmat, times, dfs)
exerciseType = FinExerciseTypes.EUROPEAN
vHW = model.bond_option(texp, strike_price, face, couponTimes, couponFlows,
exerciseType)
