def batesdetjump_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': 1.0,
'rho': -.6,
'lambda': .1,
'nu': -.5,
'delta': 0.3
}
process = BatesProcess(risk_free_ts, dividend_ts, spot, ival['v0'],
ival['kappa'], ival['theta'], ival['sigma'],
ival['rho'], ival['lambda'], ival['nu'],
ival['delta'])
model = BatesDetJumpModel(process)
engine = BatesDetJumpEngine(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('BatesDetJumpModel calibration:')
print(
'v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: %f nu: %f \
delta: %f\nkappaLambda: %f thetaLambda: %f' %
(model.v0, model.kappa, model.theta, model.sigma, model.rho,
model.Lambda, model.nu, model.delta, 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, 'BatesDetJump')
def batesdetjump_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': 1.0, 'rho': -.6, 'lambda': .1,
'nu': -.5, 'delta': 0.3}
process = BatesProcess(
risk_free_ts, dividend_ts, spot, ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process)
engine = BatesDetJumpEngine(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('BatesDetJumpModel calibration:')
print('v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: %f nu: %f \
delta: %f\nkappaLambda: %f thetaLambda: %f' %
(model.v0, model.kappa, model.theta, model.sigma,
model.rho, model.Lambda, model.nu, model.delta,
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, 'BatesDetJump')
def test_simulate_batesDetJumpModel(self):
model = BatesDetJumpModel(self.bates_process)
paths = 4
steps = 10
horizon = 1
seed = 12345
tolerance = 1.e-3
res = simulateBatesDetJumpModel(model, paths, steps, horizon, seed)
time = res[0, :]
time_expected = np.arange(0, 1.1, .1)
simulations = res[1:, :].T
np.testing.assert_array_almost_equal(time, time_expected, decimal=4)
def test_bates_det_jump(self):
# this looks like a bug in QL:
# Bates Det Jump model does not have sigma as parameter, yet
# changing sigma changes the result!
settlement_date = today()
self.settings.evaluation_date = settlement_date
daycounter = ActualActual()
exercise_date = settlement_date + 6 * Months
payoff = PlainVanillaPayoff(Put, 1290)
exercise = EuropeanExercise(exercise_date)
option = VanillaOption(payoff, exercise)
risk_free_ts = flat_rate(0.02, daycounter)
dividend_ts = flat_rate(0.04, daycounter)
spot = 1290
ival = {'delta': 3.6828677022272715e-06,
'kappa': 19.02581428347027,
'kappaLambda': 1.1209758060939223,
'lambda': 0.06524550732595163,
'nu': -1.8968106563601956,
'rho': -0.7480898462264719,
'sigma': 1.0206363887835108,
'theta': 0.01965384459461113,
'thetaLambda': 0.028915397380738218,
'v0': 0.06566800935242285}
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_1 = option.net_present_value
ival['sigma'] = 1.e-6
process = BatesProcess(
risk_free_ts, dividend_ts, SimpleQuote(spot),
ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'], ival['rho'],
ival['lambda'], ival['nu'], ival['delta'])
model = BatesDetJumpModel(process,
ival['kappaLambda'], ival['thetaLambda'])
engine = BatesDetJumpEngine(model, 64)
option.set_pricing_engine(engine)
calc_2 = option.net_present_value
if(abs(calc_1-calc_2) > 1.e-5):
print('calc 1 %f calc 2 %f' % (calc_1, calc_2))
self.assertNotEqual(calc_1, calc_2)