def zbt_libor_yield(instruments,
yields,
pricing_date,
basis='Actual/Actual (Bond)',
compounding_freq='Continuous',
maturity_dates=None):
"""
Bootstrap a zero-coupon curve from libor rates and swap yields
Args:
instruments: list of instruments, of the form Libor?M for Libor rates
and Swap?Y for swap rates
yields: market rates
pricing_date: the date where market data is observed. Settlement
is by default 2 days after pricing_date
Optional:
compounding_frequency: ... of zero-coupon rates. By default:
'Continuous'
Returns:
zero_rate: zero-coupon rate
maturity_date: ... of corresponding rate
"""
calendar = TARGET()
settings = Settings()
# must be a business day
eval_date = calendar.adjust(pydate_to_qldate(pricing_date))
settings.evaluation_date = eval_date
rates = dict(zip(instruments, yields))
ts = make_term_structure(rates, pricing_date)
cnt = DayCounter.from_name(basis)
if maturity_dates is None:
# schedule of maturity dates from settlement date to last date on
# the term structure
s = Schedule(effective_date=ts.reference_date,
termination_date=ts.max_date,
tenor=Period(1, Months),
calendar=TARGET())
maturity_dates = [qldate_to_pydate(dt) for dt in s.dates()]
cp_freq = Compounding[compounding_freq]
zc = [
ts.zero_rate(pydate_to_qldate(dt),
day_counter=cnt,
compounding=cp_freq).rate for dt in maturity_dates
]
return (maturity_dates, zc)
def zbt_libor_yield(instruments, yields, pricing_date,
basis='Actual/Actual (Bond)',
compounding_freq='Continuous',
maturity_dates=None):
"""
Bootstrap a zero-coupon curve from libor rates and swap yields
Args:
insruments: list of instruments, of the form Libor?M for Libor rates
and Swap?Y for swap rates
yields: market rates
pricing_date: the date where market data is observed. Settlement
is by default 2 days after pricing_date
Optional:
compounding_frequency: ... of zero-coupon rates. By default:
'Continuous'
Returns:
zero_rate: zero-coupon rate
maturity_date: ... of corresponding rate
"""
calendar = TARGET()
settings = Settings()
# must be a business day
eval_date = calendar.adjust(pydate_to_qldate(pricing_date))
settings.evaluation_date = eval_date
rates = dict(zip(instruments, yields))
ts = make_term_structure(rates, pricing_date)
cnt = DayCounter.from_name(basis)
if maturity_dates is None:
# schedule of maturity dates from settlement date to last date on
# the term structure
s = Schedule(effective_date=ts.reference_date,
termination_date=ts.max_date,
tenor=Period(1, Months),
calendar=TARGET())
maturity_dates = [qldate_to_pydate(dt) for dt in s.dates()]
cp_freq = compounding_from_name(compounding_freq)
zc = [ts.zero_rate(date=pydate_to_qldate(dt),
day_counter=cnt,
compounding=cp_freq).rate for dt in maturity_dates]
return (maturity_dates, zc)
dtI = dtObs[range(0, len(dtObs) - 1, 60)]
days = [
10, 30, 90, 182, 365, 365 * 2, 365 * 3, 365 * 5, 365 * 10, 365 * 15
]
# maturity in columns, observation days in rows
zc_rate = np.empty((len(dtI), len(days)), dtype='float64')
dt_maturity = np.empty_like(zc_rate, dtype='object')
# one observation date at a time, construct a term structure from
# deposit and swap rates, then compute zero-coupon rates at
# selected maturities
for i, obs_date in enumerate(dtI):
print(obs_date)
rates = df_libor.xs(obs_date) / 100.0
ts = make_term_structure(rates, obs_date)
(dt_maturity[i, ], zc_rate[i, ]) = zero_rate(ts, days, obs_date)
# PCA on rate change
zc_pca = ml.PCA(np.diff(zc_rate, axis=0))
fig = plt.figure()
fig.set_size_inches(10, 6)
ax = fig.add_subplot(121)
dtMin = dt_maturity[0, 0]
dtMax = dt_maturity[-1, -1]
ax.set_xlim(dtMin, dtMax)
ax.set_ylim(0.0, 0.1)
dtI = dtObs[range(0, len(dtObs) - 1, 60)]
days = [10, 30, 90, 182, 365, 365 * 2, 365 * 3,
365 * 5, 365 * 10, 365 * 15]
# maturity in columns, observation days in rows
zc_rate = np.empty((len(dtI), len(days)), dtype='float64')
dt_maturity = np.empty_like(zc_rate, dtype='object')
# one observation date at a time, construct a term structure from
# deposit and swap rates, then compute zero-coupon rates at
# selected maturities
for i, obs_date in enumerate(dtI):
print(obs_date)
rates = df_libor.xs(obs_date) / 100
ts = make_term_structure(rates, obs_date)
(dt_maturity[i, ], zc_rate[i, ]) = zero_rate(ts, days, obs_date)
# PCA on rate change
zc_pca = ml.PCA(np.diff(zc_rate, axis=0))
fig = plt.figure()
fig.set_size_inches(10, 6)
ax = fig.add_subplot(121)
dtMin = dt_maturity[0, 0]
dtMax = dt_maturity[-1, -1]
ax.set_xlim(dtMin, dtMax)
ax.set_ylim(0.0, 0.1)