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risk_free_ts = flat_rate(interest_rate, daycounter)
dividend_ts = flat_rate(dividend_yield, daycounter)
s0 = SimpleQuote(100.0)
# Heston model
v0 = 0.05
kappa = 5.0;
theta = 0.05;
sigma = 1.0e-4;
rho = -0.5;
discretization = QUADRATICEXPONENTIALMARTINGALE
process = HestonProcess(risk_free_ts, dividend_ts, s0, v0,
kappa, theta, sigma, rho, discretization)
#
# The simulation
# --------------
#
# The *simulate* function is not part of Quantlib. It has been added to the pyQL interface (see folder quantlib/sim). This illustrates how to crerate extensions to Quantlib and expose them to python.
#
import pylab as pl
from quantlib.sim.simulate import simulateHeston
# simulate and plot Heston paths
paths = 2
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 \
"""
# 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' %
# 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': 1.0, '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 = BatesDoubleExpModel(process)
engine = BatesDoubleExpEngine(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('BatesDoubleExpModel calibration:')
print('v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: %f \
calibrate heston model
"""
tmp = make_helpers(df_option)
risk_free_ts = tmp['risk_free_rate']
dividend_ts = tmp['dividend_rate']
spot = tmp['spot']
options = tmp['options']
# initial values for parameters
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' %
def heston_pricer(dtTrade, df_option, params, df_rates, spot):
"""
price a list of European options with heston model
"""
spot = SimpleQuote(spot)
risk_free_ts = dfToZeroCurve(df_rates['iRate'], dtTrade)
dividend_ts = dfToZeroCurve(df_rates['dRate'], dtTrade)
process = HestonProcess(
risk_free_ts, dividend_ts, spot, params['v0'], params['kappa'],
params['theta'], params['sigma'], params['rho'])
model = HestonModel(process)
engine = AnalyticHestonEngine(model, 64)
DtSettlement = dateToQLDate(dtTrade)
settings = Settings()
settings.evaluation_date = DtSettlement
calendar = TARGET()
model_value = np.zeros(len(df_option))
daycounter = ActualActual()