def test_replication_bull_spread(self):
data = util.get_real(1)
min_put_range = 1e-10
init_swap_rate = data[0]
max_call_range = 10.0
data = util.get_real(2)
option_maturity = data[0]
swap_rate_vol = data[1]
data = sorted(util.get_real(2, min_put_range, max_call_range))
lower_strike = data[0]
upper_strike = data[1]
pricer_helper = analytic_formula.BlackSwaptionPricerHelper()
call_pricer = pricer_helper.make_payers_swaption_wrt_strike(
init_swap_rate, 1.0, option_maturity, swap_rate_vol)
put_pricer = pricer_helper.make_receivers_swaption_wrt_strike(
init_swap_rate, 1.0, option_maturity, swap_rate_vol)
def analytic_func(init_swap_rate):
inner_payoff = max(init_swap_rate - lower_strike, 0.0)
return min(inner_payoff, upper_strike)
def analytic_lower_from_put_term_delta(init_swap_rate):
return put_pricer(lower_strike)
def analytic_upper_from_put_term_delta(init_swap_rate):
return put_pricer(upper_strike)
def analytic_lower_from_call_term_delta(init_swap_rate):
return call_pricer(lower_strike)
def analytic_upper_from_call_term_delta(init_swap_rate):
return call_pricer(upper_strike)
analytic_funcs = [analytic_func]
if min_put_range <= lower_strike <= init_swap_rate:
analytic_funcs.append(analytic_lower_from_put_term_delta)
if min_put_range <= upper_strike <= init_swap_rate:
analytic_funcs.append(analytic_upper_from_put_term_delta)
if init_swap_rate <= lower_strike <= max_call_range:
analytic_funcs.append(analytic_lower_from_call_term_delta)
if init_swap_rate <= upper_strike <= max_call_range:
analytic_funcs.append(analytic_upper_from_call_term_delta)
put_integrands = []
call_integrands = []
self.target = target.AnalyticReplication(call_pricer, put_pricer,
analytic_funcs,
call_integrands,
put_integrands)
actual = self.target.eval(init_swap_rate, min_put_range,
max_call_range)
expect = call_pricer(lower_strike) - call_pricer(upper_strike)
assert expect == approx(actual)
def setup(self):
self.target = target.BlackSwaptionPricerHelper()
pass
def linear_annuity_bull_spread_pricer(init_swap_rate, swap_annuity,
vol_swap_rate, swap_fixing_date,
vol_forward_fx, corr_forward_fx,
cms_lower_strike, cms_upper_strike,
cms_gearing, alpha0, alpha1):
payoff_params = {
"lower_strike": cms_lower_strike,
"upper_strike": cms_upper_strike,
"gearing": cms_gearing,
}
swap_rate_cdf = pricer_quanto_cms.make_cdf_black_swaption(
init_swap_rate=init_swap_rate,
swap_annuity=swap_annuity,
option_maturity=swap_fixing_date,
vol=vol_swap_rate)
swap_rate_pdf = pricer_quanto_cms.make_pdf_black_swaption(
init_swap_rate=init_swap_rate,
swap_annuity=swap_annuity,
option_maturity=swap_fixing_date,
vol=vol_swap_rate)
swap_rate_pdf_fprime = pricer_quanto_cms.make_pdf_fprime_black_swaption(
init_swap_rate=init_swap_rate,
swap_annuity=swap_annuity,
option_maturity=swap_fixing_date,
vol=vol_swap_rate)
annuity_mapping_params = {"alpha0": alpha0, "alpha1": alpha1}
forward_fx_diffusion_params = {
"time": swap_fixing_date,
"vol": vol_forward_fx,
"corr": corr_forward_fx,
"swap_rate_cdf": swap_rate_cdf,
"swap_rate_pdf": swap_rate_pdf,
"swap_rate_pdf_fprime": swap_rate_pdf_fprime,
"is_inverse": True
}
payer_pricer_params = {
"init_swap_rate": init_swap_rate,
"swap_annuity": swap_annuity,
"option_maturity": swap_fixing_date,
"vol": vol_swap_rate,
}
bs_pricer = analytic_formula.BlackSwaptionPricerHelper()
payer_pricer = bs_pricer.make_payers_swaption_wrt_strike(
**payer_pricer_params)
receiver_pricer_params = {
"init_swap_rate": init_swap_rate,
"swap_annuity": swap_annuity,
"option_maturity": swap_fixing_date,
"vol": vol_swap_rate
}
receiver_pricer = bs_pricer.make_receivers_swaption_wrt_strike(
**receiver_pricer_params)
discount_factor = 1.0
price = pricer_quanto_cms.replicate(init_swap_rate,
discount_factor,
payer_pricer,
receiver_pricer,
"bull_spread",
payoff_params,
forward_fx_diffusion_params,
"linear",
annuity_mapping_params,
min_put_range=1e-16,
max_call_range=0.040)
return price