def bates_calibration(df_option, ival=None):
"""
calibrate bates' model
"""
tmp = make_helpers(df_option)
risk_free_ts = tmp['risk_free_rate']
dividend_ts = tmp['dividend_rate']
spot = tmp['spot']
options = tmp['options']
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 = BatesModel(process)
engine = BatesEngine(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('model calibration results:')
print('v0: %f kappa: %f theta: %f sigma: %f\nrho: %f lambda: \
%f nu: %f delta: %f' % (model.v0, model.kappa, model.theta, model.sigma,
model.rho, model.Lambda, model.nu, model.delta))
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, 'Bates')
def test_batest_process(self):
pb = BatesProcess(self.risk_free_ts, self.dividend_ts, self.s0,
self.v0, self.kappa, self.theta, self.sigma,
self.rho, self.Lambda, self.nu, self.delta)
self.assertIsNotNone(pb)
mb = BatesModel(pb)
self.assertIsNotNone(mb)
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 setUp(self):
self.settings = Settings()
daycounter = ActualActual()
interest_rate = .1
dividend_yield = .04
self.risk_free_ts = flat_rate(interest_rate, daycounter)
self.dividend_ts = flat_rate(dividend_yield, daycounter)
s0 = SimpleQuote(32.0)
# Heston model
v0 = 0.05
kappa = 5.0
theta = 0.05
sigma = 1.0e-4
rho = -0.5
self.heston_process = HestonProcess(self.risk_free_ts,
self.dividend_ts, s0, v0, kappa,
theta, sigma, rho,
PartialTruncation)
v0 = 0.05
ival = {
'v0': v0,
'kappa': 3.7,
'theta': v0,
'sigma': 1.0,
'rho': -.6,
'lambda': .1,
'nu': -.5,
'delta': 0.3
}
spot = SimpleQuote(1200)
self.bates_process = BatesProcess(self.risk_free_ts, self.dividend_ts,
spot, ival['v0'], ival['kappa'],
ival['theta'], ival['sigma'],
ival['rho'], ival['lambda'],
ival['nu'], ival['delta'])
a = 0.376739
sigma = 0.0209
self.hullwhite_process = HullWhiteProcess(self.risk_free_ts, a, sigma)
plot(time, simulations)
show()
ival = {
'v0': v0,
'kappa': 3.7,
'theta': v0,
'sigma': 1.0,
'rho': -.6,
'lambda': .1,
'nu': -.5,
'delta': 0.3
}
spot = SimpleQuote(1200)
proc_bates = BatesProcess(risk_free_ts, dividend_ts, spot, ival['v0'],
ival['kappa'], ival['theta'], ival['sigma'],
ival['rho'], ival['lambda'], ival['nu'],
ival['delta'])
model_bates = BatesModel(proc_bates)
res_bates = simulateBates(model_bates, paths, steps, horizon, seed)
time = res_bates[0, :]
simulations = res_bates[1:, :].T
figure()
plot(time, simulations)
show()
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)