def bond_yield_spread(FV,c,T,rate,intensities,R,freq=4,t=0,freq2=0,y0=0.0,**options):
r"""
Parameters:
----------
`FV` : float,int
face value of the (risky) bond
`c` : float
annual coupon rate
`rate`: float, int or tuple of lists
Represents the zero-rate curve
Returns:
--------
`y2`: the non-risky bond yield
`y1`: the risky bond yield
`y2` - `y1`: the credit spread (`s`)
"""
from risky_bond_prices2 import risky_bond_price
from bond_duration import bond_yield
price1 = risky_bond_price(FV,c,T,rate,intensities,R,freq,t,freq2)
price2 = risky_bond_price(FV,c,T,rate,0,R,freq,t,freq2)
y1 = bond_yield(FV,c,T,rate,freq,t,freq2,price1,y0)
y2 = bond_yield(FV,c,T,rate,freq,t,freq2,price2,y0)
return y2,y1,y1-y2
def test_yield_bond2():
import numpy as np
FV = 100
rates = ([1/12,2/12,3/12,6/12,9/12,1,2,3],[x/100 for x in [0.5,0.7,1.2,\
1.4,1.7,2.1,2.3,2.5]])
coupons = [0, 0, 0, 0.04, 0.04, 0.06, 0.06, 0.08]
freqs = [1, 1, 1, 2, 2, 4, 4, 2]
times = rates[0]
afp = [
bond_price(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
"afp = arbitrage free prices"
mkt_prices = [98.5, 99, 99.5, 100.5, 101.7, 102.5, 104.5, 105.5]
yields = [
bond_yield(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
yields2 = [bond_yield(FV,coupons[i],times[i],rates,freqs[i],0,0,mkt_prices[i]\
) for i in range(len(freqs))]
durations = [bond_duration(FV,coupons[i],times[i],mkt_prices[i],freqs[i]) \
for i in range(len(freqs))]
durations2 = [bond_duration(FV,coupons[i],times[i],afp[i],freqs[i])\
for i in range(len(freqs))]
modified_durations = [bond_duration(FV,coupons[i],times[i],mkt_prices[i],freqs[i],\
0,1,Modified = 'YES') for i in range(len(freqs))]
modified_durations2 = [bond_duration(FV,coupons[i],times[i],afp[i],freqs[i],\
0,1,Modified = 'YES') for i in range(len(freqs))]
print(durations)
print(durations2)
print(modified_durations)
print(modified_durations2)
def bond_price_test5():
FV = 100
rates = ([1/12,2/12,3/12,6/12,9/12,1,2,3],[x/100 for x in [0.5,0.7,1.2,\
1.4,1.7,2.1,2.3,2.5]])
coupons = [0,0,0,0.04,0.04,0.06,0.06,0.08]
freqs = [1,1,1,2,2,4,4,2]
times = rates[0]
afp = [bond_price(FV,coupons[i],times[i],rates,freqs[i]) for i in range(len(freqs))]
"arbitrage free price"
mkt_prices = [98.5,99,99.5,100.5,101.7,102.5,104.5,105.5]
yields = [bond_yield(FV,coupons[i],times[i],rates,freqs[i]) for i in range(len(freqs))]
yields2 = [bond_yield(FV,coupons[i],times[i],rates,freqs[i],0,0,mkt_prices[i]\
) for i in range(len(freqs))]
print("Arbitrage free prices:",afp)
print("Treasury yields:",yields)
print("Realized yields:",yields2)
def test_pricing_bond():
import numpy as np
FV, c, freq = 100, 0.1, 4
print(bond_price(FV, c, 1, 0.05, freq))
print(
bond_yield(FV, c, 1, ([0.25, 0.5, 0.75, 1], [0.02, 0.03, 0.04, 0.05]),
freq))
def test_yield_bond3():
FV = 100
rates = ([1/12,2/12,3/12,6/12,9/12,1,2,3],[x/100 for x in [0.5,0.7,1.2,\
1.4,1.7,2.1,2.3,2.5]])
coupons = [0, 0, 0, 0.04, 0.04, 0.06, 0.06, 0.08]
freqs = [1, 1, 1, 2, 2, 4, 4, 2]
times = rates[0]
afp = [
bond_price(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
"afp = arbitrage free prices"
mkt_prices = [98.5, 99, 99.5, 100.5, 101.7, 102.5, 104.5, 105.5]
yields = [
bond_yield(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
yields2 = [bond_yield(FV,coupons[i],times[i],rates,freqs[i],0,0,mkt_prices[i]\
) for i in range(len(freqs))]
durations = [bond_duration(FV,coupons[i],times[i],mkt_prices[i],freqs[i]) \
for i in range(len(freqs))]
durations2 = [bond_duration(FV,coupons[i],times[i],afp[i],freqs[i])\
for i in range(len(freqs))]
modified_durations = [bond_duration(FV,coupons[i],times[i],mkt_prices[i],freqs[i],\
0,1,Modified = 'YES') for i in range(len(freqs))]
modified_durations2 = [bond_duration(FV,coupons[i],times[i],afp[i],freqs[i],\
0,1,Modified = 'YES') for i in range(len(freqs))]
d = {'Zero rates':rates[1],'No-arb prices':afp,'Market price':mkt_prices,\
'Treasury yields':yields,'Implied yields':yields2}
d2 = {'No-arb prices':afp,'Duration':durations2,'Modified duration':modified_durations2,\
'Market price':mkt_prices,'Implied duration':durations,\
'Implied modified duration':modified_durations}
import pandas as pd
#new_index = pd.DataFrame.set_index(['1M','2M','3M','6M','9M','1Y','2Y','3Y'])
indexes = ['1M', '2M', '3M', '6M', '9M', '1Y', '2Y', '3Y']
df = pd.DataFrame(data=d)
df.index = indexes
df2 = pd.DataFrame(data=d2)
df2.index = indexes
print(df)
writer = pd.ExcelWriter('output.xlsx')
df.to_excel(writer, 'Sheet1')
df2.to_excel(writer, 'Sheet2')
writer.save()
def test_yield():
FV, c, freq = 100, 0.05, 4
import numpy as np
mkt_prices = np.linspace(98, 105, 15, endpoint=True)
lifetimes = np.linspace(0.25, 3.75, 15, endpoint=True)
yields = [bond_yield(FV,c,lifetimes[i],0,freq,0,mkt_prices[i])\
for i in range(len(lifetimes))]
import matplotlib.pyplot as plt
plt.plot(lifetimes, [yields[i] for i in range(len(lifetimes))])
plt.xlabel('Maturity')
plt.ylabel('Yield')
plt.title('Yield curve from Market prices')
plt.grid(True)
print(yields)
def test_bond_yield():
FV, c, T, freq = 100, 0.06, 2, 2
import numpy as np
import matplotlib.pyplot as plt
e1,e2,e3,e4 = np.array([1,0.5,0.2,0]),np.array([0,1,0.5,0.2]),np.array([0.2,0,1,0.5]),\
np.array([1,0,0,0.2])
rate = (np.array([0.5, 1, 1.5, 2]), np.array([0.035, 0.04, 0.055, 0.06]))
g1 = lambda x: bond_yield(FV, c, T, (rate[0].tolist(),
(rate[1] + x * e1).tolist()), freq)
g2 = lambda x: bond_yield(FV, c, T, (rate[0].tolist(),
(rate[1] + x * e2).tolist()), freq)
g3 = lambda x: bond_yield(FV, c, T, (rate[0].tolist(),
(rate[1] + x * e3).tolist()), freq)
g4 = lambda x: bond_yield(FV, c, T, (rate[0].tolist(),
(rate[1] + x * e4).tolist()), freq)
div = np.linspace(0.001, 0.05, 50, endpoint=True)
plt.subplot(221)
plt.suptitle('Influence of component-wise shifts')
plt.plot(div * 100, [g1(x) * 100 for x in div])
plt.xlabel('change in r1 (%)')
plt.ylabel('Bond yield(%)')
plt.grid(True)
plt.subplot(222)
plt.plot(div * 100, [g2(x) * 100 for x in div])
plt.xlabel('change in r2 (%)')
plt.ylabel('Bond yield(%)')
plt.grid(True)
plt.subplot(223)
plt.plot(div * 100, [g3(x) * 100 for x in div])
plt.xlabel('change in r3 (%)')
plt.ylabel('Bond yield(%)')
plt.grid(True)
plt.subplot(224)
plt.plot(div * 100, [g4(x) * 100 for x in div])
plt.xlabel('change in r4 (%)')
plt.ylabel('Bond yield(%)')
plt.grid(True)
def test_yield_zero_curve():
rates = ([x / 12 for x in [1, 2, 3, 6, 9, 12]],
[x / 100 for x in [0.5, 1, 1.5, 2, 2.5, 3]])
FV, c, freq = 100, 0.24, 12
yields = [
bond_yield(FV, c, rates[0][i], rates, freq)
for i in range(len(rates[1]))
]
print(rates[0])
import numpy as np
f1 = lambda x: np.interp(x, rates[0], rates[1])
f2 = lambda x: np.interp(x, rates[0], yields)
import matplotlib.pyplot as plt
div = np.linspace(0, 2, 21, endpoint=True)
plt.plot(div, [f1(x) * 100 for x in div], label='zero-rate curve')
plt.plot(div, [f2(x) * 100 for x in div], label='treasury yield curve')
plt.xlabel('time (years)')
plt.ylabel('zero/yield curve (%)')
plt.title('Treasury yield curve vs. zero-rate curve')
plt.grid(True)
plt.legend()
def test_yield_bond1():
import numpy as np
FV = 100
rates = ([1/12,2/12,3/12,6/12,9/12,1,2,3],[x/100 for x in [0.5,0.7,1.2,\
1.4,1.7,2.1,2.3,2.5]])
coupons = [0, 0, 0, 0.04, 0.04, 0.06, 0.06, 0.08]
freqs = [1, 1, 1, 2, 2, 4, 4, 2]
times = rates[0]
afp = [
bond_price(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
"afp = arbitrage free prices"
mkt_prices = [98.5, 99, 99.5, 100.5, 101.7, 102.5, 104.5, 105.5]
yields = [
bond_yield(FV, coupons[i], times[i], rates, freqs[i])
for i in range(len(freqs))
]
yields2 = [bond_yield(FV,coupons[i],times[i],rates,freqs[i],0,0,mkt_prices[i]\
) for i in range(len(freqs))]
f = lambda x, i: (np.array(rates[1]) + x * np.eye(1, 8, i)).tolist()[0]
g = lambda x: (np.array(rates[1]) + x * np.ones((1, 8))).tolist()[0]
yields3 = [bond_yield(FV,coupons[i],times[i],(rates[0],g(0.001)),freqs[i]\
) for i in range(len(freqs))]
yields4 = [bond_yield(FV,coupons[i],times[i],(rates[0],f(0.005,0)),freqs[i]\
) for i in range(len(freqs))]
yields5 = [bond_yield(FV,coupons[i],times[i],(rates[0],f(0.005,7)),freqs[i]\
) for i in range(len(freqs))]
import matplotlib.pyplot as plt
my_xticks = ['1', '2', '3', '6', '9', '12', '24', '36']
plt.figure(1)
plt.xticks(rates[0], my_xticks)
plt.plot(rates[0],
np.array(yields) * 100,
'go--',
label='Treasury yield curve')
plt.plot(rates[0],
np.array(yields3) * 100,
'ro--',
label='Treasury yield curve: + 10bs')
plt.title('Parallel shift of the treasury curve')
plt.xlabel('Maturity (months)')
plt.ylabel('Yield (treasury)')
plt.legend()
plt.grid(True)
plt.show()
plt.figure(2)
plt.xticks(rates[0], my_xticks)
plt.plot(rates[0],
np.array(yields) * 100,
'go--',
label='Treasury yield curve')
plt.plot(rates[0],
np.array(yields4) * 100,
'ro--',
label='Treasury yield curve: + 50bs')
plt.title('1M rate increase with 50 bps')
plt.xlabel('Maturity (months)')
plt.ylabel('Yield (treasury)')
plt.legend()
plt.grid(True)
plt.show()
plt.figure(3)
plt.xticks(rates[0], my_xticks)
plt.plot(rates[0],
np.array(yields) * 100,
'go--',
label='Treasury yield curve')
plt.plot(rates[0],
np.array(yields5) * 100,
'ro--',
label='Treasury yield curve: + 50bs')
plt.title('3Y rate increase with 50 bps')
plt.xlabel('Maturity (months)')
plt.ylabel('Yield (treasury)')
plt.legend()
plt.grid(True)
plt.show()
1,
0.5,
freq2=1,
option="clean price"))
print(
bond_price(100,
0.06,
3, ([1, 2, 3], [0.08, 0.09, 0.1]),
1,
0.5,
freq2=1,
option="dirty price"))
print(
bond_yield(100,
0.06,
3, ([1, 2, 3], [0.08, 0.09, 0.1]),
1,
freq2=1,
y0=0.0))
#%%
print(bond_yield(100, 0.05, 3, freq=1, freq2=1, mkt_price=100.65))
print(bond_yield(100, 0.02, 3, freq=1, freq2=1, mkt_price=100.25))
#%%
print(bond_yield(100, 0.08, 10, freq=1, freq2=1, mkt_price=85.5030))
print(bond_price(100, 0.08, 9, 0.1040, freq=1, freq2=1))
#%%
PV1 = 5 / 1.0305 + 5 / 1.0305**2 + 105 / 1.0305**3
PV2 = 5 / 1.0295 + 5 / 1.0295**2 + 105 / 1.0295**3
app_mod_dur = (PV2 - PV1) / (2 * 0.0005 * 105.657223)
print(app_mod_dur)
#%%
x = 1 / (1 + 0.02)
def YTM(self, rate=None, t=0, freq2=0, mkt_price=None, y0=0.0, **options):
return bond_yield(self.FV,self.c,self.T,rate,self.freq,t,freq2,\
mkt_price,y0,option = options.get("option"))
