Nelson-Siegel and Svensson Bond curve fitting

NS SS bond curve.py

@@ -0,0 +1,132 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Nov 12 10:12:45 2018
+
+@author: Shinhyunjin
+"""
+
+"""
+Topic: Nelson-Siegel Curve Smoothing Technique
+Sources: Generating a Yield Curve with Nelson-Seigel Method in Excel -> https://www.youtube.com/watch?v=GsZRJmDcDbY
+         Data fitting using fmin -> http://glowingpython.blogspot.it/2011/05/curve-fitting-using-fmin.html
+
+Comment: Refer to the above video for an explanation of the method.  Also see https://github.com/MaximumBeings/public/blob/master/NSSandNS.txt
+         for an MS Excel version of the NSS and NS method.  Though the code works very
+         well, we noticed that the Excel version fitted our original data better because the solver in Excel is pretty powerful.  Nonetheless,
+         this is a very good implementation of the NSS method.  We try to fit the curve by minimizing the sum of squared errors using the
+         NS formula.  It is an iterative method that tries to guess the values for the NS parameters so you need to try different initial
+         values.  Feed the program with a set of initial values and observe the curve plot and change the parameters to get better fits. A good
+         starting set of initial values is array([0.01,0.01,0.01,1.00]) but can be changed to get a better fit.
+"""
+
+
+
+import pylab
+from numpy import *
+from scipy.optimize import fmin
+import pandas as pd
+import os
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+### Nelson - Siegel ###
+
+pre1 = os.path.dirname(os.path.realpath('C:/Users/Shinhyunjin/Dropbox/hw1data.xlsx'))
+fname1 = 'hw1data.xlsx'
+path1 = os.path.join(pre1, fname1)
+df1 = pd.read_excel(path1)
+data = pd.DataFrame(df1)
+
+
+#print ""
+# parametric function, x is the independent variable
+# and c are the parameters.
+# it's a polynomial of degree 2
+fp = lambda c, x: c[0]+(c[1]+c[2])*(c[3]/x)*(1-exp(-x/c[3])-c[2]*exp(-x/c[3]))
+
+# error function to minimize
+e = lambda p, x, y: ((fp(p,x)-y)**2).sum()
+
+
+# generating data with noise
+
+y = np.array(data['YTM']/100)  #The periods for which data are available, skip the periods with empty rate
+x = np.array(data['TAU'])  #Available rates only
+
+# fitting the data with fmin
+p0 = array([0.01,0.01,0.01,1.00])  # initial parameter value
+p = fmin(e, p0, args=(x,y))
+c = p
+j=[]
+
+for h in x:
+    j.append(c[0]+(c[1]+c[2])*(c[3]/h)*(1-exp(-h/c[3])-c[2]*exp(-h/c[3])))
+
+
+#print ""
+print ('Initial Parameters: ', p0)
+print ('Estimated Parameters: ', p)
+
+
+
+#To display interpolated data.
+h = x
+rateTable = pd.DataFrame.from_items([('Period', h),('NS', j)])
+print(rateTable.to_string())
+
+#xx = 
+pylab.plot(x,y, 'b')
+pylab.plot(x, fp(p,x), 'ro')
+pylab.title('Nelson-Siegel')
+pylab.show()
+
+
+
+#### Svensson ####
+
+# parametric function, x is the independent variable
+# and c are the parameters.
+# it's a polynomial of degree 2
+fp2 = lambda c2, x: (c2[0])+ (c2[1]*((1- exp(-x/c2[4]))/(x/c2[4])))+ (c2[2]*((((1-exp(-x/c2[4]))/(x/c2[4])))- (exp(-x/c2[4]))))+ (c2[3]*((((1-exp(-x/c2[5]))/(x/c2[5])))- (exp(-x/c2[5]))))
+real_p = array([0.02,0.01,0.01,0.01,1.00,1.00])
+
+# error function to minimize
+e2 = lambda p2, x, y: ((fp2(p2,x)-y)**2).sum()
+
+# generating data with noise
+
+# fitting the data with fmin
+p02 = array([0.01,0.01,0.01,0.01,0.01,1.00,1.00])  # initial parameter value
+p2 = fmin(e2, p02, args=(x,y))
+c2 = p2
+j2=[]
+for h2 in x:
+    j2.append((c2[0])+ (c2[1]*((1- exp(-h2/c2[4]))/(h2/c2[4])))+ (c2[2]*((((1-exp(-h2/c2[4]))/(h2/c2[4])))- (exp(-h2/c2[4]))))+ (c2[3]*((((1-exp(-h2/c2[5]))/(h2/c2[5])))- (exp(-h2/c2[5])))))
+
+print ('Initial Parameters: ', p02)
+
+print ('Estimated Parameters: ', p2)
+
+
+#To display interpolated data.
+
+h2 = x
+rateTable = pd.DataFrame.from_items([('Period', h2),('NSS', j2)])
+print(rateTable.to_string())
+
+
+#xx = array([1,2,5,10,25,30])
+plt.title('Result')
+plt.grid(True)
+plt.plot(x, y, 'g')
+plt.plot(x, fp2(p2,x), '--', label = 'SS')
+plt.plot(x, fp2(p2,x), 'bo')
+plt.plot(x, fp(p,x), 'ro')
+plt.plot(x, fp(p,x), ':', label = 'NS')
+plt.legend(loc=0)
+plt.xlabel('Mat')
+plt.ylabel('YTM')
+
+plt.show()
+

sswtioil.csv

@@ -0,0 +1,244 @@
+date,close,volume
+2018-11-09,21860,38677
+2018-11-08,22235,13358
+2018-11-07,22240,7751
+2018-11-06,22625,26615
+2018-11-05,22615,10842
+2018-11-02,22950,12808
+2018-11-01,23370,6178
+2018-10-31,23895,10443
+2018-10-30,24180,7659
+2018-10-29,24235,5681
+2018-10-26,23985,8381
+2018-10-25,23915,3319
+2018-10-24,23985,30060
+2018-10-23,24875,2859
+2018-10-22,25055,3311
+2018-10-19,24840,6769
+2018-10-18,25115,7725
+2018-10-17,25920,3739
+2018-10-16,25725,9848
+2018-10-15,25820,2893
+2018-10-12,25790,6459
+2018-10-11,25915,8100
+2018-10-10,26880,4190
+2018-10-08,26560,19906
+2018-10-05,26910,5151
+2018-10-04,27395,25589
+2018-10-02,27260,28117
+2018-10-01,26430,13509
+2018-09-28,25975,2115
+2018-09-27,26030,38746
+2018-09-21,25320,1977
+2018-09-20,25605,19900
+2018-09-19,25055,5205
+2018-09-18,24625,2965
+2018-09-17,24740,2189
+2018-09-14,24650,3961
+2018-09-13,25065,14313
+2018-09-12,25040,9086
+2018-09-11,24265,1571
+2018-09-10,24495,1035
+2018-09-07,24390,1391
+2018-09-06,24600,3038
+2018-09-05,24785,3732
+2018-09-04,25215,2212
+2018-09-03,25005,2401
+2018-08-31,25180,13915
+2018-08-30,25005,42834
+2018-08-29,24575,61957
+2018-08-28,24630,4604
+2018-08-27,24585,17955
+2018-08-24,24530,12493
+2018-08-23,24350,14580
+2018-08-22,23720,4000
+2018-08-21,23555,9907
+2018-08-20,23375,543
+2018-08-17,23275,5454
+2018-08-16,23165,35758
+2018-08-14,24000,9871
+2018-08-13,24035,27421
+2018-08-10,23625,16041
+2018-08-09,23815,24546
+2018-08-08,24565,2391
+2018-08-07,24590,1668
+2018-08-06,24390,26440
+2018-08-03,24490,2027
+2018-08-02,24095,4039
+2018-08-01,24280,5034
+2018-07-31,24760,26428
+2018-07-30,24520,1124
+2018-07-27,24665,1766
+2018-07-26,24645,2762
+2018-07-25,24430,6838
+2018-07-24,24070,23609
+2018-07-23,24190,2353
+2018-07-20,24270,15085
+2018-07-19,24020,4506
+2018-07-18,23735,23613
+2018-07-17,23785,5200
+2018-07-16,24615,4096
+2018-07-13,24650,6027
+2018-07-12,24735,10228
+2018-07-11,25600,9351
+2018-07-10,25795,2815
+2018-07-09,25760,2351
+2018-07-06,25475,5964
+2018-07-05,25680,8114
+2018-07-04,25960,19263
+2018-07-03,26035,5424
+2018-07-02,25525,27808
+2018-06-29,25505,19344
+2018-06-28,25235,6776
+2018-06-27,24595,14079
+2018-06-26,23765,7281
+2018-06-25,23775,9001
+2018-06-22,23050,1696
+2018-06-21,22755,1670
+2018-06-20,22830,2120
+2018-06-19,22660,2353
+2018-06-18,22305,6302
+2018-06-15,23220,1451
+2018-06-14,23090,682
+2018-06-12,23010,621
+2018-06-11,22795,1134
+2018-06-08,22840,7277
+2018-06-07,22595,3759
+2018-06-05,22565,3629
+2018-06-04,22820,1678
+2018-06-01,23250,2010
+2018-05-31,23645,3313
+2018-05-30,23130,1806
+2018-05-29,23120,3887
+2018-05-28,23100,8572
+2018-05-25,24470,3888
+2018-05-24,24855,2566
+2018-05-23,25005,6238
+2018-05-21,24950,11257
+2018-05-18,24895,11549
+2018-05-17,24870,5268
+2018-05-16,24690,5601
+2018-05-15,24565,6343
+2018-05-14,24435,6537
+2018-05-11,24720,8108
+2018-05-10,24885,8937
+2018-05-09,24345,7149
+2018-05-08,24285,6686
+2018-05-04,23720,962
+2018-05-03,23485,2803
+2018-05-02,23435,2796
+2018-04-30,23535,1647
+2018-04-27,23565,1430
+2018-04-26,23670,2115
+2018-04-25,23480,5683
+2018-04-24,24000,2118
+2018-04-23,23660,1547
+2018-04-20,23660,4875
+2018-04-19,23830,2664
+2018-04-18,23275,1393
+2018-04-17,23080,2418
+2018-04-16,23145,3024
+2018-04-13,23160,6079
+2018-04-12,23180,11824
+2018-04-11,22570,33607
+2018-04-10,22215,3054
+2018-04-09,21600,15288
+2018-04-06,21850,355
+2018-04-05,22035,522
+2018-04-04,21880,27127
+2018-04-03,21850,3569
+2018-04-02,22575,703
+2018-03-30,22390,497
+2018-03-29,22375,2782
+2018-03-28,22360,1300
+2018-03-27,22720,7760
+2018-03-26,22675,845
+2018-03-23,22520,1114
+2018-03-22,22525,16781
+2018-03-21,21960,5399
+2018-03-20,21635,1099
+2018-03-19,21445,11645
+2018-03-16,21180,1390
+2018-03-15,21095,3923
+2018-03-14,21010,3437
+2018-03-13,21220,937
+2018-03-12,21375,4300
+2018-03-09,20835,2573
+2018-03-08,21155,1377
+2018-03-07,21445,823
+2018-03-06,21620,1857
+2018-03-05,21250,944
+2018-03-02,21065,13615
+2018-02-28,21660,1602
+2018-02-27,22015,1321
+2018-02-26,22000,1772
+2018-02-23,21630,3356
+2018-02-22,21065,1132
+2018-02-21,21100,2858
+2018-02-20,21440,1009
+2018-02-19,21470,17845
+2018-02-14,20425,1613
+2018-02-13,20555,2965
+2018-02-12,20610,1933
+2018-02-09,20880,14094
+2018-02-08,21265,6084
+2018-02-07,21935,5776
+2018-02-06,21850,10332
+2018-02-05,22380,2315
+2018-02-02,22745,4872
+2018-02-01,22320,2122
+2018-01-31,22005,4318
+2018-01-30,22315,9906
+2018-01-29,22825,6765
+2018-01-26,22510,2785
+2018-01-25,22835,6897
+2018-01-24,22190,2394
+2018-01-23,22030,3597
+2018-01-22,21800,2579
+2018-01-19,21720,4515
+2018-01-18,22030,3831
+2018-01-17,21930,9339
+2018-01-16,22175,8404
+2018-01-15,22185,4435
+2018-01-12,21820,3494
+2018-01-11,21845,4932
+2018-01-10,21850,9899
+2018-01-09,21385,2203
+2018-01-08,21180,3327
+2018-01-05,21320,1647
+2018-01-04,21380,16966
+2018-01-03,20770,7894
+2018-01-02,20895,3411
+2017-12-28,20535,3463
+2017-12-27,20515,9791
+2017-12-26,20155,4842
+2017-12-22,20030,4635
+2017-12-21,19995,7034
+2017-12-20,19885,1499
+2017-12-19,19765,673
+2017-12-18,19830,5575
+2017-12-15,19720,3386
+2017-12-14,19555,6769
+2017-12-13,19855,1442
+2017-12-12,20135,2307
+2017-12-11,19700,5892
+2017-12-08,19520,2279
+2017-12-07,19325,15604
+2017-12-06,19775,1261
+2017-12-05,19790,3119
+2017-12-04,19960,559
+2017-12-01,19865,5407
+2017-11-30,19805,21065
+2017-11-29,19840,41557
+2017-11-28,19880,1899
+2017-11-27,20190,23006
+2017-11-24,20160,3308
+2017-11-23,19955,6844
+2017-11-22,19905,8028
+2017-11-21,19475,1062
+2017-11-20,19580,2896
+2017-11-17,19145,807
+2017-11-16,19145,428
+2017-11-15,19060,6791
+2017-11-14,19565,3999
+2017-11-13,19625,6933