def test_basisswap_pv_zero_if_onecurve_termstructure():
notl = 1e8
dt_start = dt_val
leg6m = IborLeg.from_tenor(dt_start, length, frequency=6, notional=notl)
leg3m = IborLeg.from_tenor(dt_start, length, frequency=3, notional=-notl)
basis_swap = Swap(leg3m, leg6m)
mkt_1crv = RatesTermStructure(dt_val, {curr: {'discount': crv_disc}})
pv_6m_1crv = present_value(leg6m, mkt_1crv, curr)
pv_3m_1crv = present_value(leg3m, mkt_1crv, curr)
pv_1crv = present_value(basis_swap, mkt_1crv, curr)
assert np.isclose(pv_6m_1crv, notl)
assert np.isclose(pv_3m_1crv, -notl)
assert np.isclose(pv_1crv, 0.0)
spread = 0.005 # 5 basis point spread
crv_6m = DiscountCurveWithNodes(dt_val,
node_dates,
node_rates + spread,
interpolator=interpolator,
extrapolate=('clamped', 'natural'))
mkt_2crv = RatesTermStructure(dt_val,
{curr: {
'discount': crv_disc,
6: crv_6m
}})
pv_2crv = present_value(basis_swap, mkt_2crv, curr)
assert not np.isclose(pv_2crv, 0.0)
def test_iborleg():
"""Test equality of various construction calls"""
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=notional,
fixing_lag=2)
# from_frame
annuity_from_frame = Annuity.from_frame(float_leg.frame)
assert annuity_from_frame != float_leg
fixed_leg_from_frame = FixedLeg.from_frame(float_leg.frame)
assert fixed_leg_from_frame != float_leg
ibor_leg_from_frame = IborLeg.from_frame(float_leg.frame)
assert ibor_leg_from_frame == float_leg
# init
annuity_init = Annuity(float_leg.frame)
assert annuity_init != float_leg
fixed_leg_init = FixedLeg(float_leg.frame)
assert annuity_init != float_leg
ibor_leg_init = IborLeg(float_leg.frame)
assert ibor_leg_init == float_leg
def test_iborleg():
"""Test equality of various construction calls"""
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=notional, fixing_lag=2)
# from_frame
annuity_from_frame = Annuity.from_frame(float_leg.frame)
assert annuity_from_frame != float_leg
fixed_leg_from_frame = FixedLeg.from_frame(float_leg.frame)
assert fixed_leg_from_frame != float_leg
ibor_leg_from_frame = IborLeg.from_frame(float_leg.frame)
assert ibor_leg_from_frame == float_leg
# init
annuity_init = Annuity(float_leg.frame)
assert annuity_init != float_leg
fixed_leg_init = FixedLeg(float_leg.frame)
assert annuity_init != float_leg
ibor_leg_init = IborLeg(float_leg.frame)
assert ibor_leg_init == float_leg
def test_present_value_vanilla_ibor_leg_at_fixing_date_equals_notional():
"""Confirm spot starting Iborleg with Notional Exchange is worth par
This is a canonical result of funding at ibor.
Though there are two curves, both discount and ibor curves are equal.
"""
# Constant Curves
zero_spread = 0.0
crv_ibor_no_spread = ConstantDiscountRateCurve(dt_valuation=dt_val,
zero_rate=rate_discount +
zero_spread,
daycount_conv='30360',
currency=curr)
curves = {curr: {'discount': crv_discount, frqncy: crv_ibor_no_spread}}
two_constant_curves = RatesTermStructure.from_curve_map(dt_val, curves)
spot_starting = IborLeg.from_tenor(dt_settlement=dt_val,
tenor=length,
frequency=frqncy,
rate=np.nan,
notional=-notional,
fixing_lag=0)
pv_flt = present_value(spot_starting, two_constant_curves, curr)
assert np.isclose(pv_flt, -notional)
# Nodal Curves
assert np.isclose(present_value(spot_starting, nodal_rates_market, curr),
-notional)
def strip_of_swaps(dt_settlement, currency, tenor, maturities, rates):
"""Strip / List of Swaps of increasing length and a single currency and tenor
These strips are used to calibrate nodes in discount and forward curves.
If we are interested in pricing derivatives that depends on rates of two
different frequencies (eg 3M & 12M), we will need one strip per frequency.
Curve
TODO Business date treatment
TODO Add proper conventions
"""
idx = np.arange(len(maturities))
fixed_legs = [
FixedLeg.from_tenor(dt_settlement,
maturities[i],
tenor,
rates[i],
currency=currency) for i in idx
]
float_legs = [
IborLeg.from_tenor(dt_settlement,
maturities[i],
tenor,
notional=-1.,
currency=currency) for i in idx
]
swaps = [VanillaSwap(fixed_legs[i], float_legs[i]) for i in idx]
return swaps
def test_fixing_lag():
"""Ensure lag of 2 provides minimum of 2 days lag.
This is under default business day adjustment.
"""
# Todo - what is the default business day adjustment???
leg_no_lag = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-1 * notional, fixing_lag=0)
leg_lag = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-1 * notional, fixing_lag=2)
assert np.all(leg_lag.frame['fixing'] >
leg_no_lag.frame['fixing'] + pd.Timedelta(days=1))
def test_swap():
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=notional)
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-1 * notional, fixing_lag=2)
swap = Swap(fixed_leg, float_leg)
assert swap.leg_receive == fixed_leg
assert swap.leg_pay == float_leg
def test_vanilla_swap():
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=notional, currency='EUR')
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-1 * notional, currency='EUR')
swap = VanillaSwap(fixed_leg, float_leg)
assert swap.leg_receive == fixed_leg
assert swap.leg_pay == float_leg
def par_rate(contract, market):
df_fixed = contract.leg_fixed.frame.copy()
df_fixed.rate = 1.0
df_fixed.notional *= -1
annuity = FixedLeg.from_frame(df_fixed, notl_exchange=False)
df_float = contract.leg_float.frame.copy()
floating_no_xch = IborLeg.from_frame(df_float, notl_exchange=False)
ccy = contract.leg_fixed.currency
assert ccy == contract.leg_float.currency
pv_fix = present_value(annuity, market, ccy)
pv_flt = present_value(floating_no_xch, market, ccy)
return pv_flt / pv_fix
def par_rate(contract, market):
df_fixed = contract.leg_fixed.frame.copy()
df_fixed.rate = 1.0
df_fixed.notional *= -1
annuity = FixedLeg.from_frame(df_fixed, notl_exchange=False)
df_float = contract.leg_float.frame.copy()
floating_no_xch = IborLeg.from_frame(df_float, notl_exchange=False)
ccy = contract.leg_fixed.currency
assert ccy == contract.leg_float.currency
pv_fix = present_value(annuity, market, ccy)
pv_flt = present_value(floating_no_xch, market, ccy)
return pv_flt / pv_fix
def test_fixing_lag():
"""Ensure lag of 2 provides minimum of 2 days lag.
This is under default business day adjustment.
"""
# Todo - what is the default business day adjustment???
leg_no_lag = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-1 * notional,
fixing_lag=0)
leg_lag = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-1 * notional,
fixing_lag=2)
assert np.all(leg_lag.frame['fixing'] > leg_no_lag.frame['fixing'] +
pd.Timedelta(days=1))
def test_basisswap_pv_zero_if_onecurve_termstructure():
notl = 1e8
dt_start = dt_val
leg6m = IborLeg.from_tenor(dt_start, length, frequency=6, notional=notl)
leg3m = IborLeg.from_tenor(dt_start, length, frequency=3, notional=-notl)
basis_swap = Swap(leg3m, leg6m)
mkt_1crv = RatesTermStructure(dt_val, {curr: {'discount': crv_disc}})
pv_6m_1crv = present_value(leg6m, mkt_1crv, curr)
pv_3m_1crv = present_value(leg3m, mkt_1crv, curr)
pv_1crv = present_value(basis_swap, mkt_1crv, curr)
assert np.isclose(pv_6m_1crv, notl)
assert np.isclose(pv_3m_1crv, -notl)
assert np.isclose(pv_1crv, 0.0)
spread = 0.005 # 5 basis point spread
crv_6m = DiscountCurveWithNodes(dt_val, node_dates, node_rates + spread,
interpolator=interpolator,
extrapolate=('clamped', 'natural'))
mkt_2crv = RatesTermStructure(dt_val, {curr: {'discount': crv_disc,
6: crv_6m}})
pv_2crv = present_value(basis_swap, mkt_2crv, curr)
assert not np.isclose(pv_2crv, 0.0)
def test_present_value_of_swap_after_expiry():
dt_settle = dt_val - pd.Timedelta(days=1000)
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=notional)
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-notional, fixing_lag=0)
pv_fix = present_value(fixed_leg, simple_rates_market, curr)
assert np.isclose(pv_fix, 0.0)
pv_flt = present_value(float_leg, simple_rates_market, curr)
assert np.isclose(pv_flt, 0.0)
def test_swap():
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=notional)
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-1 * notional,
fixing_lag=2)
swap = Swap(fixed_leg, float_leg)
assert swap.leg_receive == fixed_leg
assert swap.leg_pay == float_leg
def test_vanilla_swap():
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=notional,
currency='EUR')
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-1 * notional,
currency='EUR')
swap = VanillaSwap(fixed_leg, float_leg)
assert swap.leg_receive == fixed_leg
assert swap.leg_pay == float_leg
def test_present_value_of_swap_after_expiry():
dt_settle = dt_val - pd.Timedelta(days=1000)
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=notional)
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-notional,
fixing_lag=0)
pv_fix = present_value(fixed_leg, simple_rates_market, curr)
assert np.isclose(pv_fix, 0.0)
pv_flt = present_value(float_leg, simple_rates_market, curr)
assert np.isclose(pv_flt, 0.0)
def test_present_value_vanilla_ibor_leg_at_fixing_date_equals_notional():
"""Confirm spot starting Iborleg with Notional Exchange is worth par
This is a canonical result of funding at ibor.
Though there are two curves, both discount and ibor curves are equal.
"""
# Constant Curves
zero_spread = 0.0
crv_ibor_no_spread = ConstantDiscountRateCurve(
dt_valuation=dt_val, zero_rate=rate_discount + zero_spread,
daycount_conv='30360', currency=curr)
curves = {curr: {'discount': crv_discount, frqncy: crv_ibor_no_spread}}
two_constant_curves = RatesTermStructure.from_curve_map(dt_val, curves)
spot_starting = IborLeg.from_tenor(dt_settlement=dt_val, tenor=length,
frequency=frqncy, rate=np.nan,
notional=-notional, fixing_lag=0)
pv_flt = present_value(spot_starting, two_constant_curves, curr)
assert np.isclose(pv_flt, -notional)
# Nodal Curves
assert np.isclose(present_value(spot_starting,nodal_rates_market, curr),
-notional)
fixed_leg.frame.currency.iloc[0]: {
'discount': crv_discount,
frqncy: crv_ibor
}
}
simple_rates_market = RatesTermStructure.from_curve_map(dt_val, curve_map)
# 2. Test IborLeg
# Hack up what the frame might look like
df_fixed = fixed_leg.frame
df_float = df_fixed.copy()
df_float.type = 'IBOR'
df_float['fixing'] = df_fixed.start
df_float['frequency'] = frqncy
df_float.notional *= -1
float_leg = IborLeg.from_frame(df_float)
# Calculate Forward Rates for each ibor cash flow
forwards = ibor_rate(float_leg, simple_rates_market)
# 3. Test VanillaSwap
swap = VanillaSwap(fixed_leg, float_leg)
# 4. Test pricing
print('pv fixed_leg = {}'.format(
present_value(fixed_leg, simple_rates_market, curr)))
print('pv float_leg = {}'.format(
present_value(float_leg, simple_rates_market, curr)))
print('pv swap = {}'.format(present_value(swap, simple_rates_market,
curr)))
print('forward rates = {}'.format(forwards))
notional = 100
dcc = '30360'
fixed_legs, float_legs, swaps = [], [], []
for i in mkt_ids:
fixed_legs.append(
FixedLeg.from_tenor(dt_settle,
durations[i],
frqncy,
fixed_rates[i],
notional=notional,
currency=curr))
float_legs.append(
IborLeg.from_tenor(dt_settle,
durations[i],
frqncy,
notional=-1 * notional,
currency=curr))
swaps.append(VanillaSwap(fixed_legs[i], float_legs[i]))
market_portfolio = Portfolio.of_trades(swaps)
# 3. Create Market. Specify number of curves to use, and the interpolators
interpolator = CubicSplineWithNodeSens # CubicSplineWithNodeSens, PiecewiseLinear
n_curves = 2
accrual_fn = daycounter(dcc)
node_dates = []
for i in range(n_contracts): # final pay date of each swap
node_dates.append(fixed_legs[i].frame.pay.iloc[-1])
node_dates = pd.Series(node_dates)
length = 24 # months
frqncy = 6 # months
fixed_rate = 0.03
notional = 100
curr = "USD"
payment_lag = 2 # days
# 1. Create a Vanilla Swap
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=notional)
# Note that fixed rates are provided to IborLeg. In pricing, only those in the
# past will be used. Others will be replaced by their Forward rates.
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle, tenor=length,
frequency=frqncy, rate=fixed_rate,
notional=-notional, fixing_lag=0)
swap = VanillaSwap(fixed_leg, float_leg)
# 2. Create Market with Ibor and Discount Curves - both with Constant Rates
rate_discount = 0.05
crv_discount = ConstantDiscountRateCurve(
dt_valuation=dt_val, zero_rate=rate_discount,
daycount_conv='30360', currency=curr)
spread = 0.002
crv_disc = ConstantDiscountRateCurve( # Dummy IBOR Curve
dt_valuation=dt_val, zero_rate=rate_discount + spread,
daycount_conv='30360', currency=curr)
crv_ibor = ConstantDiscountRateCurve( # Dummy IBOR Curve
dt_valuation=dt_val, zero_rate=rate_discount + spread,
daycount_conv='30360', currency=curr)
curve_map = {fixed_leg.frame.currency.iloc[0]:
{'discount': crv_discount, frqncy: crv_ibor}}
simple_rates_market = RatesTermStructure.from_curve_map(dt_val, curve_map)
# 2. Test IborLeg
# Hack up what the frame might look like
df_fixed = fixed_leg.frame
df_float = df_fixed.copy()
df_float.type = 'IBOR'
df_float['fixing'] = df_fixed.start
df_float['frequency'] = frqncy
df_float.notional *= -1
float_leg = IborLeg.from_frame(df_float)
# Calculate Forward Rates for each ibor cash flow
forwards = ibor_rate(float_leg, simple_rates_market)
# 3. Test VanillaSwap
swap = VanillaSwap(fixed_leg, float_leg)
# 4. Test pricing
print('pv fixed_leg = {}'.format(present_value(fixed_leg, simple_rates_market, curr)))
print('pv float_leg = {}'.format(present_value(float_leg, simple_rates_market, curr)))
print('pv swap = {}'.format(present_value(swap, simple_rates_market, curr)))
print('forward rates = {}'.format(forwards))
print('swap rate = {}'.format(par_rate(swap, simple_rates_market)))
fixed_rate = 0.03
notional = 100
curr = "USD"
payment_lag = 2 # days
# 1. Create a Vanilla Swap
fixed_leg = FixedLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=notional)
# Note that fixed rates are provided to IborLeg. In pricing, only those in the
# past will be used. Others will be replaced by their Forward rates.
float_leg = IborLeg.from_tenor(dt_settlement=dt_settle,
tenor=length,
frequency=frqncy,
rate=fixed_rate,
notional=-notional,
fixing_lag=0)
swap = VanillaSwap(fixed_leg, float_leg)
# 2. Create Market with Ibor and Discount Curves - both with Constant Rates
rate_discount = 0.05
crv_discount = ConstantDiscountRateCurve(dt_valuation=dt_val,
zero_rate=rate_discount,
daycount_conv='30360',
currency=curr)
spread = 0.002
crv_disc = ConstantDiscountRateCurve( # Dummy IBOR Curve
dt_valuation=dt_val,