def _blsimpv(price, spot, strike, risk_free_rate, time, option_type, dividend):
spot = SimpleQuote(spot)
daycounter = ActualActual(ISMA)
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), .3, daycounter)
process = BlackScholesMertonProcess(spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
accuracy = 0.001
max_evaluations = 1000
min_vol = 0.01
max_vol = 2
vol = option.implied_volatility(price, process, accuracy, max_evaluations,
min_vol, max_vol)
return vol
def _blsprice(spot,
strike,
risk_free_rate,
time,
volatility,
option_type='Call',
dividend=0.0,
calc='price'):
"""
Black-Scholes option pricing model + greeks.
"""
_spot = SimpleQuote(spot)
daycounter = ActualActual(ISMA)
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), volatility,
daycounter)
process = BlackScholesMertonProcess(_spot, dividend_ts, risk_free_ts,
volatility_ts)
exercise_date = today() + Period(time * 365, Days)
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
if calc == 'price':
res = option.npv
elif calc == 'delta':
res = option.delta
elif calc == 'gamma':
res = option.gamma
elif calc == 'theta':
res = option.theta
elif calc == 'rho':
res = option.rho
elif calc == 'vega':
res = option.vega
elif calc == 'lambda':
res = option.delta * spot / option.npv
else:
raise ValueError('calc type %s is unknown' % calc)
return res
def test_mc_variance_swap(self):
""" test mc variance engine vs expected result
"""
vols = []
dates = []
interm_date = self.today + int(0.1 * 365 + 0.5)
exercise = EuropeanExercise(self.ex_date)
dates.append(interm_date)
dates.append(self.ex_date)
vols.append(0.1)
vols.append(self.values['v'])
# Exercising code using BlackVarianceCurve because BlackVarianceSurface
# is unreliable. Result should be v*v for arbitrary t1 and v1
# (as long as 0<=t1<t and 0<=v1<v)
vol_ts = BlackVarianceCurve(self.today, dates, vols, self.dc, True)
stoch_process = BlackScholesMertonProcess(self.spot, self.q_ts,
self.r_ts, vol_ts)
engine = MCVarianceSwapEngine(
stoch_process,
time_steps_per_year=250,
required_samples=1023,
seed=42,
)
variance_swap = VarianceSwap(
self.values['type'],
self.values['strike'],
self.values['nominal'],
self.today,
self.ex_date,
)
variance_swap.set_pricing_engine(engine)
calculated = variance_swap.variance
expected = 0.04
tol = 3.0e-4
error = abs(calculated - expected)
self.assertTrue(error < tol)
def setUp(self):
self.settings = Settings()
self.calendar = NullCalendar()
self.todays_date = Date(15, May, 1998)
self.settlement_date = Date(17, May, 1998)
self.settings.evaluation_date = self.todays_date
# options parameters
self.dividend_yield = 0.00
self.risk_free_rate = 0.06
self.volatility = 0.25
self.spot = SimpleQuote(100)
self.maturity = Date(17, May, 1999)
self.daycounter = Actual365Fixed()
self.tol = 1e-2
# bootstrap the yield/dividend/vol curves
dates = [self.settlement_date] + \
[self.settlement_date + Period(i + 1, Years)
for i in range(40)]
rates = [0.01] + \
[0.01 + 0.0002 * np.exp(np.sin(i / 4.0)) for i in range(40)]
divRates = [0.02] + \
[0.02 + 0.0001 * np.exp(np.sin(i / 5.0)) for i in range(40)]
self.r_ts = ZeroCurve(dates, rates, self.daycounter)
self.q_ts = ZeroCurve(dates, divRates, self.daycounter)
self.vol_ts = BlackConstantVol(
self.settlement_date,
self.calendar,
self.volatility,
self.daycounter
)
self.black_scholes_merton_process = BlackScholesMertonProcess(
self.spot,
self.q_ts,
self.r_ts,
self.vol_ts
)
self.dates = dates
def blsprice(spot, strike, risk_free_rate, time, volatility, option_type='Call', dividend=0.0):
""" """
spot = SimpleQuote(spot)
daycounter = Actual360()
risk_free_ts = FlatForward(today(), risk_free_rate, daycounter)
dividend_ts = FlatForward(today(), dividend, daycounter)
volatility_ts = BlackConstantVol(today(), NullCalendar(), volatility, daycounter)
process = BlackScholesMertonProcess(spot, dividend_ts, risk_free_ts, volatility_ts)
exercise_date = today() + 90
exercise = EuropeanExercise(exercise_date)
payoff = PlainVanillaPayoff(option_type, strike)
option = EuropeanOption(payoff, exercise)
engine = AnalyticEuropeanEngine(process)
option.set_pricing_engine(engine)
return option.npv
def test_bsm_hw(self):
print("Testing European option pricing for a BSM process" +
" with one-factor Hull-White model...")
dc = Actual365Fixed()
todays_date = today()
maturity_date = todays_date + Period(20, Years)
settings = Settings()
settings.evaluation_date = todays_date
spot = SimpleQuote(100)
q_ts = flat_rate(todays_date, 0.04, dc)
r_ts = flat_rate(todays_date, 0.0525, dc)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), 0.25, dc)
hullWhiteModel = HullWhite(r_ts, 0.00883, 0.00526)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
exercise = EuropeanExercise(maturity_date)
fwd = spot.value * q_ts.discount(maturity_date) / \
r_ts.discount(maturity_date)
payoff = PlainVanillaPayoff(Call, fwd)
option = VanillaOption(payoff, exercise)
tol = 1e-8
corr = [-0.75, -0.25, 0.0, 0.25, 0.75]
expectedVol = [
0.217064577, 0.243995801, 0.256402830, 0.268236596, 0.290461343
]
for c, v in zip(corr, expectedVol):
bsm_hw_engine = AnalyticBSMHullWhiteEngine(c, bsm_process,
hullWhiteModel)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(bsm_hw_engine)
npv = option.npv
compVolTS = BlackConstantVol(todays_date, NullCalendar(), v, dc)
bs_process = BlackScholesMertonProcess(spot, q_ts, r_ts, compVolTS)
bsEngine = AnalyticEuropeanEngine(bs_process)
comp = VanillaOption(payoff, exercise)
comp.set_pricing_engine(bsEngine)
impliedVol = comp.implied_volatility(npv,
bs_process,
1e-10,
500,
min_vol=0.1,
max_vol=0.4)
if (abs(impliedVol - v) > tol):
print("Failed to reproduce implied volatility cor: %f" % c)
print("calculated: %f" % impliedVol)
print("expected : %f" % v)
if abs((comp.npv - npv) / npv) > tol:
print("Failed to reproduce NPV")
print("calculated: %f" % comp.npv)
print("expected : %f" % npv)
self.assertAlmostEqual(impliedVol, v, delta=tol)
self.assertAlmostEqual(comp.npv / npv, 1, delta=tol)
def test_compare_BsmHW_HestonHW(self):
"""
From Quantlib test suite
"""
print("Comparing European option pricing for a BSM " +
"process with one-factor Hull-White model...")
dc = Actual365Fixed()
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
tol = 1.e-2
spot = SimpleQuote(100)
dates = [todays_date + Period(i, Years) for i in range(40)]
rates = [0.01 + 0.0002 * np.exp(np.sin(i / 4.0)) for i in range(40)]
divRates = [0.02 + 0.0001 * np.exp(np.sin(i / 5.0)) for i in range(40)]
s0 = SimpleQuote(100)
r_ts = ZeroCurve(dates, rates, dc)
q_ts = ZeroCurve(dates, divRates, dc)
vol = SimpleQuote(0.25)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), vol.value, dc)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
variance = vol.value * vol.value
hestonProcess = HestonProcess(risk_free_rate_ts=r_ts,
dividend_ts=q_ts,
s0=s0,
v0=variance,
kappa=5.0,
theta=variance,
sigma=1e-4,
rho=0.0)
hestonModel = HestonModel(hestonProcess)
hullWhiteModel = HullWhite(r_ts, a=0.01, sigma=0.01)
bsmhwEngine = AnalyticBSMHullWhiteEngine(0.0, bsm_process,
hullWhiteModel)
hestonHwEngine = AnalyticHestonHullWhiteEngine(hestonModel,
hullWhiteModel, 128)
tol = 1e-5
strikes = [0.25, 0.5, 0.75, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5, 2.0, 4.0]
maturities = [1, 2, 3, 5, 10, 15, 20, 25, 30]
types = [Put, Call]
for type in types:
for strike in strikes:
for maturity in maturities:
maturity_date = todays_date + Period(maturity, Years)
exercise = EuropeanExercise(maturity_date)
fwd = strike * s0.value * \
q_ts.discount(maturity_date) / \
r_ts.discount(maturity_date)
payoff = PlainVanillaPayoff(type, fwd)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(bsmhwEngine)
calculated = option.npv
option.set_pricing_engine(hestonHwEngine)
expected = option.npv
if ((np.abs(expected - calculated) > calculated * tol)
and (np.abs(expected - calculated) > tol)):
cp = PAYOFF_TO_STR[type]
print("Failed to reproduce npv")
print("strike : %f" % strike)
print("maturity : %d" % maturity)
print("type : %s" % cp)
self.assertAlmostEqual(expected, calculated, delta=tol)
def test_compare_bsm_bsmhw_hestonhw(self):
dc = Actual365Fixed()
todays_date = today()
settings = Settings()
settings.evaluation_date = todays_date
tol = 1.e-2
spot = SimpleQuote(100)
dates = [todays_date + Period(i, Years) for i in range(40)]
rates = [0.01 + 0.0002 * np.exp(np.sin(i / 4.0)) for i in range(40)]
divRates = [0.02 + 0.0001 * np.exp(np.sin(i / 5.0)) for i in range(40)]
s0 = SimpleQuote(100)
r_ts = ZeroCurve(dates, rates, dc)
q_ts = ZeroCurve(dates, divRates, dc)
vol = SimpleQuote(0.25)
vol_ts = BlackConstantVol(todays_date, NullCalendar(), vol.value, dc)
bsm_process = BlackScholesMertonProcess(spot, q_ts, r_ts, vol_ts)
payoff = PlainVanillaPayoff(Call, 100)
exercise = EuropeanExercise(dates[1])
option = VanillaOption(payoff, exercise)
analytic_european_engine = AnalyticEuropeanEngine(bsm_process)
option.set_pricing_engine(analytic_european_engine)
npv_bsm = option.npv
variance = vol.value * vol.value
hestonProcess = HestonProcess(risk_free_rate_ts=r_ts,
dividend_ts=q_ts,
s0=s0,
v0=variance,
kappa=5.0,
theta=variance,
sigma=1e-4,
rho=0.0)
hestonModel = HestonModel(hestonProcess)
hullWhiteModel = HullWhite(r_ts, a=0.01, sigma=0.01)
bsmhwEngine = AnalyticBSMHullWhiteEngine(0.0, bsm_process,
hullWhiteModel)
hestonHwEngine = AnalyticHestonHullWhiteEngine(hestonModel,
hullWhiteModel, 128)
hestonEngine = AnalyticHestonEngine(hestonModel, 144)
option.set_pricing_engine(hestonEngine)
npv_heston = option.npv
option.set_pricing_engine(bsmhwEngine)
npv_bsmhw = option.npv
option.set_pricing_engine(hestonHwEngine)
npv_hestonhw = option.npv
print("calculated with BSM: %f" % npv_bsm)
print("BSM-HW: %f" % npv_bsmhw)
print("Heston: %f" % npv_heston)
print("Heston-HW: %f" % npv_hestonhw)
self.assertAlmostEqual(npv_bsm, npv_bsmhw, delta=tol)
self.assertAlmostEqual(npv_bsm, npv_hestonhw, delta=tol)
def test_replicating_variance_swap(self):
"""
data from "A Guide to Volatility and Variance Swaps",
Derman, Kamal & Zou, 1999
with maturity t corrected from 0.25 to 0.246575
corresponding to Jan 1, 1999 to Apr 1, 1999
"""
replicating_option_data = [
{
'type': OptionType.Put,
'strike': 50,
'v': 0.30
},
{
'type': OptionType.Put,
'strike': 55,
'v': 0.29
},
{
'type': OptionType.Put,
'strike': 60,
'v': 0.28
},
{
'type': OptionType.Put,
'strike': 65,
'v': 0.27
},
{
'type': OptionType.Put,
'strike': 70,
'v': 0.26
},
{
'type': OptionType.Put,
'strike': 75,
'v': 0.25
},
{
'type': OptionType.Put,
'strike': 80,
'v': 0.24
},
{
'type': OptionType.Put,
'strike': 85,
'v': 0.23
},
{
'type': OptionType.Put,
'strike': 90,
'v': 0.22
},
{
'type': OptionType.Put,
'strike': 95,
'v': 0.21
},
{
'type': OptionType.Put,
'strike': 100,
'v': 0.20
},
{
'type': OptionType.Call,
'strike': 100,
'v': 0.20
},
{
'type': OptionType.Call,
'strike': 105,
'v': 0.19
},
{
'type': OptionType.Call,
'strike': 110,
'v': 0.18
},
{
'type': OptionType.Call,
'strike': 115,
'v': 0.17
},
{
'type': OptionType.Call,
'strike': 120,
'v': 0.16
},
{
'type': OptionType.Call,
'strike': 125,
'v': 0.15
},
{
'type': OptionType.Call,
'strike': 130,
'v': 0.14
},
{
'type': OptionType.Call,
'strike': 135,
'v': 0.13
},
]
dates = [self.ex_date]
call_strikes, put_strikes, call_vols, put_vols = [], [], [], []
# Assumes ascending strikes and same min call and max put strikes
for data in replicating_option_data:
if data['type'] == OptionType.Call:
call_strikes.append(data['strike'])
call_vols.append(data['v'])
elif data['type'] == OptionType.Put:
put_strikes.append(data['strike'])
put_vols.append(data['v'])
else:
raise ValueError("unknown option type")
vols = np.zeros((len(replicating_option_data) - 1, 1))
strikes = []
for j, v in enumerate(put_vols):
vols[j][0] = v
strikes.append(put_strikes[j])
for k in range(1, len(call_vols)):
j = len(put_vols) - 1
vols[j + k][0] = call_vols[k]
strikes.append(call_strikes[k])
vols_mat = Matrix.from_ndarray(vols)
vol_ts = BlackVarianceSurface(self.today, NullCalendar(), dates,
strikes, vols_mat, self.dc)
stoch_process = BlackScholesMertonProcess(self.spot, self.q_ts,
self.r_ts, vol_ts)
engine = ReplicatingVarianceSwapEngine(stoch_process, call_strikes,
put_strikes, 5.0)
variance_swap = VarianceSwap(
self.values['type'],
self.values['strike'],
self.values['nominal'],
self.today,
self.ex_date,
)
variance_swap.set_pricing_engine(engine)
calculated = variance_swap.variance
expected = self.values['result']
self.assertAlmostEqual(calculated, expected, delta=self.values['tol'])