def call_on_zero_coupon_bond(today=None,
strike_date=None,
maturity=None,
strike_price=None,
zeros=None,
dcf_method=None,
**params):
S = dcf(today, strike_date, method=dcf_method)
T = dcf(today, maturity, method=dcf_method)
bond_S = zeros[strike_date]
bond_T = zeros[maturity]
a, b = params['k']
sigma, nu = params['nu']
rho = params['rho'][0][1]
sigma_term = np.sqrt(mini_sigma(a, b, sigma, nu, rho, 0, S, T))
factor = np.log(bond_T / (bond_S * strike_price)) / sigma_term
return bond_T * norm.cdf(factor + sigma_term /
2) - bond_S * strike_price * norm.cdf(
factor - sigma_term / 2)
def floorlet_black(bond, forward, S, T, K, sigma, method='Act360'):
dcf_factor = dcf(S, T, method=method)
vol = sigma * np.sqrt(S)
return bond * dcf_factor * blacklet(K, S, forward, vol, omega=-1)
def bond_func(maturity, **params):
maturity_in_yrs = dcf(today, maturity, method=bond_dcf)
# Here shift is purposely different than delta, which should be zero, as we prefer to do shift by
# using the extension with his shift parameter.
return BondPriceFunction(0, maturity_in_yrs, **params) * np.exp(
-params['shift'] * maturity_in_yrs)
def ZBC_func(strike_date, bond_maturity, K, **params):
market_to_strike = bond_func(strike_date, **params)
market_to_bond_maturity = bond_func(bond_maturity, **params)
S_bond = dcf(today, strike_date, method=bond_dcf)
T_bond = dcf(today, bond_maturity, method=bond_dcf)
S_opt = dcf(today, strike_date, method=ZBC_dcf)
T_opt = dcf(today, bond_maturity, method=ZBC_dcf)
ref_model_strike = BondPriceFunction(0, S_bond, **params)
ref_model_bond_maturity = BondPriceFunction(0, T_bond, **params)
modifier = market_to_bond_maturity / ref_model_bond_maturity
modified_strike = K * (market_to_strike / ref_model_strike) / modifier
return ZBCPricerFunction(0, S_opt, T_opt, modified_strike, **
params) * modifier
def in_default_func(maturity, **params):
maturity_in_yrs = dcf(today, maturity, method=bond_dcf)
# Here we do not use shift method but we use the intrisitic bond value function.
return InDefaultFunction(0, maturity_in_yrs, **params)
def test_dcf_2_x_3():
df = dcf.dcf(8.08,
growth_rates=[-0.01, -0.02],
discount_rates=[0.00, 0.01, 0.02])
expected = np.array([[799.9, 395.9], [398.0, 263.1], [263.1, 196.0]])
assert np.allclose(df.values, expected, atol=0.1)
discount_rates = [
0.00, 0.01, 0.02, 0.03, 0.04, 0.05
] # I honestly have no idea how to think about discount rates
years = [2018, 2019, 2020]
key_df = pd.DataFrame.from_records(
[
[7.5239, 7.8880, 8.0800], # billion USD
[1.333, 2.117, 4.945], # billion USD
[25.746, 28.042, 29.471], # billion USD
],
columns=[str(x) for x in years],
index=["adj_earnings", "cash", "debt"])
wt_avg_fixed_cpn = 0.0413 # see DDIS; wt_avg_yrs = 11.78
share_price = 41.06 # USD
shares = 1.86 # billion
if __name__ == '__main__':
# print(key_df)
pd.set_option('display.float_format', '{:.1f}'.format)
df = dcf.dcf(
np.mean(key_df.loc["adj_earnings"]),
growth_rates,
discount_rates,
debt=np.mean(key_df.loc["debt"]),
cash=np.mean(key_df.loc["cash"]),
debt_rate=wt_avg_fixed_cpn,
)
print(
f"Adj EPS PV: base=2018-2020, debt=naive, shares=constant, terminal-value=0\n{df / shares}"
)