def batesdoubleexpdetjump_calibration(df_option,
dtTrade=None,
df_rates=None,
ival=None):
# array of option helpers
hh = heston_helpers(df_option, dtTrade, df_rates, ival)
options = hh['options']
spot = hh['spot']
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
v0 = .02
if ival is None:
ival = {
'v0': v0,
'kappa': 3.7,
'theta': v0,
'sigma': .1,
'rho': -.6,
'lambda': .1,
'nu': -.5,
'delta': 0.3
}
process = HestonProcess(risk_free_ts, dividend_ts, spot, ival['v0'],
ival['kappa'], ival['theta'], ival['sigma'],
ival['rho'])
model = BatesDoubleExpDetJumpModel(process, 1.0)
engine = BatesDoubleExpDetJumpEngine(model, 64)
for option in options:
option.set_pricing_engine(engine)
om = LevenbergMarquardt()
model.calibrate(options, om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8))
print('BatesDoubleExpDetJumpModel calibration:')
print(
'v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: %f \
nuUp: %f nuDown: %f\np: %f\nkappaLambda: %f thetaLambda: %f' %
(model.v0, model.kappa, model.theta, model.sigma, model.rho,
model.Lambda, model.nuUp, model.nuDown, model.p, model.kappaLambda,
model.thetaLambda))
calib_error = (1.0 / len(options)) * sum(
[pow(o.calibration_error(), 2) for o in options])
print('SSE: %f' % calib_error)
return merge_df(df_option, options, 'BatesDoubleExpDetJump')
def batesdoubleexpdetjump_calibration(df_option, dtTrade=None,
df_rates=None, ival=None):
# array of option helpers
hh = heston_helpers(df_option, dtTrade, df_rates, ival)
options = hh['options']
spot = hh['spot']
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
v0 = .02
if ival is None:
ival = {'v0': v0, 'kappa': 3.7, 'theta': v0,
'sigma': .1, 'rho': -.6, 'lambda': .1,
'nu': -.5, 'delta': 0.3}
process = HestonProcess(
risk_free_ts, dividend_ts, spot, ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'])
model = BatesDoubleExpDetJumpModel(process, 1.0)
engine = BatesDoubleExpDetJumpEngine(model, 64)
for option in options:
option.set_pricing_engine(engine)
om = LevenbergMarquardt()
model.calibrate(
options, om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8)
)
print('BatesDoubleExpDetJumpModel calibration:')
print('v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: %f \
nuUp: %f nuDown: %f\np: %f\nkappaLambda: %f thetaLambda: %f' %
(model.v0, model.kappa, model.theta, model.sigma,
model.rho, model.Lambda, model.nuUp, model.nuDown,
model.p, model.kappaLambda, model.thetaLambda))
calib_error = (1.0 / len(options)) * sum(
[pow(o.calibration_error(), 2) for o in options])
print('SSE: %f' % calib_error)
return merge_df(df_option, options, 'BatesDoubleExpDetJump')
def heston_calibration(df_option, dtTrade=None, df_rates=None, ival=None):
"""
calibrate heston model
"""
# array of option helpers
print df_option, df_rates, ival
hh = heston_helpers(df_option, dtTrade, df_rates, ival)
options = hh['options']
spot = hh['spot']
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
if ival is None:
ival = {
'v0': 0.1,
'kappa': 1.0,
'theta': 0.1,
'sigma': 0.5,
'rho': -.5
}
process = HestonProcess(risk_free_ts, dividend_ts, spot, ival['v0'],
ival['kappa'], ival['theta'], ival['sigma'],
ival['rho'])
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
for option in options:
option.set_pricing_engine(engine)
om = LevenbergMarquardt(1e-8, 1e-8, 1e-8)
model.calibrate(options, om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8))
print('model calibration results:')
print('v0: %f kappa: %f theta: %f sigma: %f rho: %f' %
(model.v0, model.kappa, model.theta, model.sigma, model.rho))
calib_error = (1.0 / len(options)) * sum(
[pow(o.calibration_error() * 100.0, 2) for o in options])
print('SSE: %f' % calib_error)
return merge_df(df_option, options, 'Heston')
def heston_pricer(trade_date, options, params, rates, spot):
"""
Price a list of European options with heston model.
"""
spot = SimpleQuote(spot)
risk_free_ts = df_to_zero_curve(rates[nm.INTEREST_RATE], trade_date)
dividend_ts = df_to_zero_curve(rates[nm.DIVIDEND_YIELD], trade_date)
process = HestonProcess(risk_free_ts, dividend_ts, spot, **params)
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
settlement_date = pydate_to_qldate(trade_date)
settings = Settings()
settings.evaluation_date = settlement_date
modeled_values = np.zeros(len(options))
for index, row in options.T.iteritems():
expiry_date = row[nm.EXPIRY_DATE]
strike = row[nm.STRIKE]
option_type = Call if row[nm.OPTION_TYPE] == nm.CALL_OPTION else Put
payoff = PlainVanillaPayoff(option_type, strike)
expiry_qldate = pydate_to_qldate(expiry_date)
exercise = EuropeanExercise(expiry_qldate)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(engine)
modeled_values[index] = option.net_present_value
prices = options.filter(
items=[nm.EXPIRY_DATE, nm.STRIKE, nm.OPTION_TYPE, nm.SPOT])
prices[nm.PRICE] = modeled_values
prices[nm.TRADE_DATE] = trade_date
return prices
def heston_pricer(trade_date, options, params, rates, spot):
"""
Price a list of European options with heston model.
"""
spot = SimpleQuote(spot)
risk_free_ts = df_to_zero_curve(rates[nm.INTEREST_RATE], trade_date)
dividend_ts = df_to_zero_curve(rates[nm.DIVIDEND_YIELD], trade_date)
process = HestonProcess(risk_free_ts, dividend_ts, spot, **params)
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
settlement_date = pydate_to_qldate(trade_date)
settings = Settings()
settings.evaluation_date = settlement_date
modeled_values = np.zeros(len(options))
for index, row in options.T.iteritems():
expiry_date = row[nm.EXPIRY_DATE]
strike = row[nm.STRIKE]
option_type = Call if row[nm.OPTION_TYPE] == nm.CALL_OPTION else Put
payoff = PlainVanillaPayoff(option_type, strike)
expiry_qldate = pydate_to_qldate(expiry_date)
exercise = EuropeanExercise(expiry_qldate)
option = VanillaOption(payoff, exercise)
option.set_pricing_engine(engine)
modeled_values[index] = option.net_present_value
prices = options.filter(items=[nm.EXPIRY_DATE, nm.STRIKE,
nm.OPTION_TYPE, nm.SPOT])
prices[nm.PRICE] = modeled_values
prices[nm.TRADE_DATE] = trade_date
return prices
def heston_calibration(df_option, dtTrade=None, df_rates=None, ival=None):
"""
calibrate heston model
"""
# array of option helpers
print df_option, df_rates, ival
hh = heston_helpers(df_option, dtTrade, df_rates, ival)
options = hh['options']
spot = hh['spot']
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
if ival is None:
ival = {'v0': 0.1, 'kappa': 1.0, 'theta': 0.1,
'sigma': 0.5, 'rho': -.5}
process = HestonProcess(
risk_free_ts, dividend_ts, spot, ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'])
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
for option in options:
option.set_pricing_engine(engine)
om = LevenbergMarquardt(1e-8, 1e-8, 1e-8)
model.calibrate(
options, om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8)
)
print('model calibration results:')
print('v0: %f kappa: %f theta: %f sigma: %f rho: %f' %
(model.v0, model.kappa, model.theta, model.sigma,
model.rho))
calib_error = (1.0 / len(options)) * sum(
[pow(o.calibration_error() * 100.0, 2) for o in options])
print('SSE: %f' % calib_error)
return merge_df(df_option, options, 'Heston')
def heston_helpers(df_option, dtTrade=None, df_rates=None, ival=None):
"""
Create array of heston options helpers
"""
if dtTrade is None:
dtTrade = df_option['dtTrade'][0]
DtSettlement = pydate_to_qldate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
if df_rates is None:
df_tmp = DataFrame.filter(df_option, items=['dtExpiry', 'IR', 'IDIV'])
grouped = df_tmp.groupby('dtExpiry')
df_rates = grouped.agg(lambda x: x[0])
# convert data frame (date/value) into zero curve
# expect the index to be a date, and 1 column of values
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
# back out the spot from any forward
iRate = df_option['R'][0]
iDiv = df_option['D'][0]
TTM = df_option['T'][0]
Fwd = df_option['F'][0]
spot = SimpleQuote(Fwd * np.exp(-(iRate - iDiv) * TTM))
print('Spot: %f risk-free rate: %f div. yield: %f' % \
(spot.value, iRate, iDiv))
# loop through rows in option data frame, construct
# helpers for bid/ask
oneDay = datetime.timedelta(days=1)
dtExpiry = [dtTrade + int(t * 365) * oneDay for t in df_option['T']]
df_option['dtExpiry'] = dtExpiry
options = []
for index, row in df_option.T.iteritems():
strike = row['K']
if (strike / spot.value > 1.3) | (strike / spot.value < .7):
continue
days = int(365 * row['T'])
maturity = Period(days, Days)
options.append(
HestonModelHelper(maturity, calendar, spot.value, strike,
SimpleQuote(row['VB']), risk_free_ts,
dividend_ts, ImpliedVolError))
options.append(
HestonModelHelper(maturity, calendar, spot.value, strike,
SimpleQuote(row['VA']), risk_free_ts,
dividend_ts, ImpliedVolError))
return {'options': options, 'spot': spot}
def heston_helpers(df_option, dtTrade=None, df_rates=None, ival=None):
"""
Create array of heston options helpers
"""
if dtTrade is None:
dtTrade = df_option['dtTrade'][0]
DtSettlement = pydate_to_qldate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
if df_rates is None:
df_tmp = DataFrame.filter(df_option, items=['dtExpiry', 'IR', 'IDIV'])
grouped = df_tmp.groupby('dtExpiry')
df_rates = grouped.agg(lambda x: x[0])
# convert data frame (date/value) into zero curve
# expect the index to be a date, and 1 column of values
risk_free_ts = df_to_zero_curve(df_rates['R'], dtTrade)
dividend_ts = df_to_zero_curve(df_rates['D'], dtTrade)
# back out the spot from any forward
iRate = df_option['R'][0]
iDiv = df_option['D'][0]
TTM = df_option['T'][0]
Fwd = df_option['F'][0]
spot = SimpleQuote(Fwd * np.exp(-(iRate - iDiv) * TTM))
print('Spot: %f risk-free rate: %f div. yield: %f' % \
(spot.value, iRate, iDiv))
# loop through rows in option data frame, construct
# helpers for bid/ask
oneDay = datetime.timedelta(days=1)
dtExpiry = [dtTrade + int(t * 365) * oneDay for t in df_option['T']]
df_option['dtExpiry'] = dtExpiry
options = []
for index, row in df_option.T.iteritems():
strike = row['K']
if (strike / spot.value > 1.3) | (strike / spot.value < .7):
continue
days = int(365 * row['T'])
maturity = Period(days, Days)
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['VB']),
risk_free_ts, dividend_ts,
ImpliedVolError))
options.append(
HestonModelHelper(
maturity, calendar, spot.value,
strike, SimpleQuote(row['VA']),
risk_free_ts, dividend_ts,
ImpliedVolError))
return {'options': options, 'spot': spot}
