def test_polydyne() :
'''
test polydyne
'''
from Options.rate import rate
# time stamp
tt=0.5
# Rate list using for interpolation
Rate=list()
for i in range(8):
'''
Generate the Rate list for testing the function
r=e*tt^5+f*tt^4+a*tt^3+b*tt^2+c*tt+d
e=0.1
f=0.4
a=0.2
b=0.5
c=-0.1
d=0.1
'''
Rate.append(rate(0.1*tt**5+0.4*tt**4+0.2*tt**3+0.5*tt**2-0.1*tt+0.1,tt))
tt=tt+0.5
# the time point of the interpolated rate
ttt=2.25
print('The Real Rate:',0.1*ttt**5+0.4*ttt**4+0.2*ttt**3+0.5*ttt**2-0.1*ttt+0.1)
print('The Interpolated Rate',inpl.polydyne(Rate,t=ttt,n=5))
def test_cubic_polynomial():
'''
test cubic_polynomial
'''
from Options.rate import rate
# time stamp
tt=0.5
# Rate list using for interpolation
Rate=list()
for i in range(6):
'''
Generate the Rate list for testing the function
r=a*tt^3+b*tt^2+c*tt+d
a=0.2
b=0.5
c=-0.1
d=0.1
'''
Rate.append(rate(0.2*tt**3+0.5*tt**2-0.1*tt+0.1,tt))
tt=tt+0.5
# the time point of the interpolated rate
ttt=2.25
print('The Real Rate:',0.2*ttt**3+0.5*ttt**2-0.1*ttt+0.1)
print('The Interpolated Rate',inpl.cubic_polynomial(Rate,t=ttt))
def test_Hermit():
'''
test Hermit
'''
from Options.rate import rate
# time stamp
tt=0.5
# Rate list using for interpolation
Rate=list()
for i in range(6):
'''
Generate the Rate list for testing the function
r=a*tt^3+b*tt^2+c*tt+d
a=0.2
b=0.5
c=-0.1
d=0.1
'''
Rate.append(rate(0.2*tt**3+0.5*tt**2-0.1*tt+0.1,tt))
tt=tt+0.5
# the time point of the interpolated rate
ttt=2.25
print('The Real Rate:',0.2*ttt**3+0.5*ttt**2-0.1*ttt+0.1)
print('The Interpolated Rate',inpl.Hermit(Rate,t=ttt))
import numpy as np
a=np.linspace(0.5,3,num=100)
b=list()
for j in a:
b.append(inpl.Hermit(Rate,t=j))
import matplotlib.pyplot as plt
plt.plot(a,b)
'''
Another Example
'''
Rate=[rate(0.1047,0.5),rate(0.1054,1),rate(0.1068,1.5),rate(0.1081,2)]
print(inpl.difference(Rate[0],Rate[1],Rate[2],startpoint=True))
def test_to_forward_rate():
'''
test function: to_forward_rate
input parameters:
Maturity(years) Rate(%)
1 2.0
2 3.0
3 3.7
4 4.2
5 4.5
output parameters:
Maturity(years) Rate(%)
1-2 4.0
2-3 5.1
3-4 5.7
4-5 5.7
'''
from Options.rate import rate
print(interest_rate.to_forward_rate(rate(2.0, 1), rate(3.0, 2)))
print(interest_rate.to_forward_rate(rate(3.0, 2), rate(3.7, 3)))
print(interest_rate.to_forward_rate(rate(3.7, 3), rate(4.2, 4)))
print(interest_rate.to_forward_rate(rate(4.2, 4), rate(4.5, 5)))
def Discount_to_Rate(Discount):
import numpy as np
from Options.rate import rate
def take(elem):
return elem.maturity
Discount.sort(key=take)
def value(x):
return x.value
def maturity(x):
return x.maturity
value = list(map(value, Discount))
matur = list(map(maturity, Discount))
Rate = list()
for i in range(len(value)):
Rate.append(rate(-np.log(value[i]) / matur[i], matur[i]))
return Rate
def Rate_to_Discount(Rate):
import numpy as np
from Options.rate import rate
def take(elem):
return elem.maturity
Rate.sort(key=take)
def value(x):
return x.value
def maturity(x):
return x.maturity
value = list(map(value, Rate))
matur = list(map(maturity, Rate))
Discount = list()
for i in range(len(value)):
Discount.append(rate(np.exp(-value[i] * matur[i]), matur[i]))
return Discount
def test_NS_model():
'''
Testing NS_model
construct sample:
R(0,s)=beta_0+beta_1*(1-exp(-s/m))/(s/m)+beta_2*((1-exp(-s/m))/(s/m)-exp(-s/m))
n=15
beta_0=1.5
beta_1=-0.5
beta_2=1.0
m_0=1.0
'''
from Options.rate import rate
import numpy as np
n=15
R=list()
beta_0=1.5
beta_1=-0.5
beta_2=1.0
m_0=5.0
# Generate R
for i in range(n):
if i==0 :
R.append(rate(beta_0+beta_1,i))
elif i>0 :
R.append(rate(beta_0+beta_1*(1-np.exp(-i/m_0))/(i/m_0)+beta_2*((1-np.exp(-i/m_0))/(i/m_0)-np.exp(-i/m_0)),i))
def value(x):
return x.value
def maturity(x):
return x.maturity
value=list(map(value,R))
matur=list(map(maturity,R))
import matplotlib.pyplot as plt
plt.figure('NS model')
plt.plot(matur,value)
m=list([1.0])
t=list([1.0])
result=inpl.NS_model(R,t=t,m=m)
print('R with m=1.0:',result)
# m = None
result=inpl.NS_model(R,t=t,step_length=0.1,step=100000)
print('R with m=None:',result)
'''
n=15
beta_0=1.5
beta_1=-0.5
beta_2=1.0
beta_3=0.3
m_0=1.0
m_1=1.5
'''
# Generate R_plus
R_plus=list()
beta_3=0.3
m_1=1.5
for i in range(n):
if i==0 :
R_plus.append(rate(beta_0+beta_1,i))
elif i>0 :
R_plus.append(rate(beta_0+beta_1*(1-np.exp(-i/m_0))/(i/m_0)+beta_2*((1-np.exp(-i/m_0))/(i/m_0)-np.exp(-i/m_0))+beta_3*((1-np.exp(-i/m_1))/(i/m_1)-np.exp(-i/m_1)),i))
def value(x):
return x.value
def maturity(x):
return x.maturity
value_plus=list(map(value,R_plus))
matur_plus=list(map(maturity,R_plus))
import matplotlib.pyplot as plt
plt.figure('NSS model')
plt.plot(matur_plus,value_plus)
t=list([1.0,5.0])
result_plus=inpl.NS_model(R_plus,t=t,mtype='NSS',step_length=0.1,step=10000)
print('R_plus:',result_plus)
from Options import interpolation as inpl
import numpy as np
from Options.rate import rate
n=15
R=list()
beta_0=1.5
beta_1=-0.5
beta_2=1.0
m_0=5.0
# Generate R
for i in range(n):
if i==0 :
R.append(rate(beta_0+beta_1,i))
elif i>0 :
R.append(rate(beta_0+beta_1*(1-np.exp(-i/m_0))/(i/m_0)+beta_2*((1-np.exp(-i/m_0))/(i/m_0)-np.exp(-i/m_0)),i))
result=inpl.NS_Model(R,'NS')
a=result.NS_m_unsetted(10.0,1000,0.01)
print(a)
b=list()
for i in np.linspace(0,30,1000):
b.append(result.NS_m_unsetted_fit(list([i])))
import matplotlib.pyplot as plt
plt.plot(np.linspace(0,30,1000),b)
def test_cubic_constraint_regress():
'''
Testing cubic constraint regress
Construct the test sample
B(0,s)= a1*s^3+b1*s^2+c1*s+d1 0<s<5
a2*s^3+b2*s^2+c2*s+d2 5<s<15
a3*s^3+b3*s^2+c3*s+d3 15<s<30
generate the data
a1= 0.1 b1= 0.2 c1=-0.5 d1=1
a2= 0.2 b2=-0.5 c2= 0.3 d2=2
a3= 0.15 b3= 0.25 c3= 0.4 d3=0.5
interval 1 sample number: 10
interval 2 sample number: 8
interval 3 sample number: 3
'''
from Options.rate import rate
import numpy as np
# discounting factor
Back=list()
for i in range(10):
s=np.random.uniform(low=0.0,high=5.0,size=1)
a1=0.1
b1=0.2
c1=-0.5
d1=1
value=a1*s**3+b1*s**2+c1*s+d1+np.random.normal(scale=0.01)
Back.append(rate(value,s))
for i in range(8):
s=np.random.uniform(low=5.0,high=15.0,size=1)
a2=0.2
b2=-0.5
c2=0.3
d2=2
value=a2*s**3+b2*s**2+c2*s+d2+np.random.normal(scale=0.01)
Back.append(rate(value,s))
for i in range(10):
s=np.random.uniform(low=15.0,high=30.0,size=1)
a3=0.15
b3=0.25
c3=0.4
d3=0.5
value=a3*s**3+b3*s**2+c3*s+d3+np.random.normal(scale=0.01)
Back.append(rate(value,s))
interval=list([5,15])
# construct constraint
A=np.zeros((3+len(Back),12))
d=np.zeros((3+len(Back),1))
A[0,0]=5**3
A[0,1]=5**2
A[0,2]=5
A[0,3]=1
A[0,4]=-5**3
A[0,5]=-5**2
A[0,6]=-5
A[0,7]=-1
d[0,0]=0
A[1,4]=15**3
A[1,5]=15**2
A[1,6]=15
A[1,7]=1
A[1,8]=-15**3
A[1,9]=-15**2
A[1,10]=-15
A[1,11]=-1
d[1,0]=0
A[2,3]=1
d[2,0]=1
for i in range(10):
A[3+i,0]=Back[i].maturity**3
A[3+i,1]=Back[i].maturity**2
A[3+i,2]=Back[i].maturity
A[3+i,3]=1
d[3+i,0]=Back[i].value
for i in range(8):
A[13+i,4]=Back[10+i].maturity**3
A[13+i,5]=Back[10+i].maturity**2
A[13+i,6]=Back[10+i].maturity
A[13+i,7]=1
d[13+i,0]=Back[10+i].value
for i in range(3):
A[21+i,8]=Back[18+i].maturity**3
A[21+i,9]=Back[18+i].maturity**2
A[21+i,10]=Back[18+i].maturity
A[21+i,11]=1
d[21+i,0]=Back[18+i].value
constraint=list([A,d])
result=inpl.cubic_constraint_regress(Back)
result.cubic_constraint_regress(interval=interval,constraint_or_not=True)
fit=result.fit(0.1)
# result=result.cubic_constraint_regress()
def value(x):
return x.value
def maturity(x):
return x.maturity
value=list(map(value,Back))
matur=list(map(maturity,Back))
import matplotlib.pyplot as plt
plt.plot(matur,value)
matur_simu=np.linspace(0,30,1000)
value_simu=list()
for i in matur_simu :
value_simu.append(result.fit(i))
plt.plot(matur_simu,value_simu)
return fit
def test_cubic_spline():
'''
test cubic spline
'''
from Options.rate import rate
# time stamp
tt=0.5
# Rate list using for interpolation
Rate=list()
for i in range(6):
'''
Generate the Rate list for testing the function
r=a*tt^3+b*tt^2+c*tt+d
a=0.2
b=0.5
c=-0.1
d=0.1
'''
Rate.append(rate(0.2*tt**3+0.5*tt**2-0.1*tt+0.1,tt))
tt=tt+0.5
# the time point of the interpolated rate
ttt=2.25
print('The Real Rate:',0.2*ttt**3+0.5*ttt**2-0.1*ttt+0.1)
print('The Interpolated Rate:',inpl.cubic_spline(Rate,t=ttt))
import numpy as np
a=np.linspace(0.5,3,num=100)
b=list()
for j in a:
b.append(inpl.cubic_spline(Rate,t=j))
import matplotlib.pyplot as plt
plt.figure('The Natural Condition')
plt.plot(a,b,label='inter')
from scipy.interpolate import CubicSpline
def value(x):
return x.value
def maturity(x):
return x.maturity
'''
using scipy.interpolate.CubicSpline
parameters are setted
bc_type='natural' : the second boudary condition
extrapolate='bool' : the boudary point satisfies the inner interpolated function
print and plot the result
'''
cs=CubicSpline(list(map(maturity,Rate)),list(map(value,Rate)),bc_type='natural',extrapolate='bool')
print('The scipy Rate:',cs(ttt))
plt.plot(list(map(maturity,Rate)),list(map(value,Rate)),'o',label='data')
plt.plot(a,cs(a),label='scipy')
plt.legend()
plt.figure('The Clamped Condition')
c=list()
for j in a:
c.append(inpl.cubic_spline(Rate,t=j,bc='continue'))
import matplotlib.pyplot as plt
plt.plot(a,c,label='inter')
cs=CubicSpline(list(map(maturity,Rate)),list(map(value,Rate)),bc_type='clamped')
print('The scipy Rate:',cs(ttt))
plt.plot(list(map(maturity,Rate)),list(map(value,Rate)),'o',label='data')
plt.plot(a,cs(a),label='scipy')
plt.legend()