From 82e48b5131786ad63463ad177a8656ee71173d19 Mon Sep 17 00:00:00 2001
From: MFEshinhyunjin <42334069+MFEshinhyunjin@users.noreply.github.com>
Date: Tue, 13 Nov 2018 14:47:41 +0900
Subject: [PATCH] Nelson-Siegel and Svensson Bond curve fitting

Nelson-Siegel and Svensson Bond curve fitting with Python
---
 NS SS bond curve.py | 132 ++++++++++++++++++++++++
 sswtioil.csv        | 244 ++++++++++++++++++++++++++++++++++++++++++++
 sswtioil.xlsx       | Bin 0 -> 16384 bytes
 3 files changed, 376 insertions(+)
 create mode 100644 NS SS bond curve.py
 create mode 100644 sswtioil.csv
 create mode 100644 sswtioil.xlsx

diff --git a/NS SS bond curve.py b/NS SS bond curve.py
new file mode 100644
index 0000000..034c277
--- /dev/null
+++ b/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()
+
diff --git a/sswtioil.csv b/sswtioil.csv
new file mode 100644
index 0000000..2bf9e04
--- /dev/null
+++ b/sswtioil.csv
@@ -0,0 +1,244 @@
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