import matplotlib.pylab as plt

x = [1, 3, 6, 12]
y = [2.12029, 2.73757, 3.31129, 3.89643]
plt.stem(x, y)
x_n = 8
y_n = (y[3]-y[2])/(x[3]-x[2]) * (x_n - x[2]) + y[2]
plt.stem(x_n, y_n, '--ro')
plt.annotate(f'{x_n} months (interp.)', [x_n+0.2, y_n])
print(f'The Libor rate for {x_n} month(s) is {y_n}.')

The Libor rate for 8 month(s) is 3.506336666666667.

import numpy as np
Fs = 10.0 # Hz
F0 = 1.0 # Hz
print(f'Discrete frequency: {F0/Fs} samples per second.')
x = np.arange(-5, 6)/Fs # two periods for tan, one period for sine/cosine
y = np.sin(2*np.pi*F0*x)
plt.stem(x, y)

Discrete frequency: 0.1 samples per second.

<StemContainer object of 3 artists>

upsampling_factor = 5 # increase the sampling frequency by 5
Fs_p = upsampling_factor*Fs    
y_p = np.zeros(int(len(x)*Fs_p/Fs))
y_p[::int(Fs_p/Fs)] = y
x_p = np.arange(-len(y_p)/2, len(y_p)/2)/Fs_p # one period of the signal
plt.stem(x_p, y_p)

<StemContainer object of 3 artists>

def isocelesTriangle(x): 
    return 1.0-np.abs(x) if np.abs(x)<=1 else 0

def isocelesTriangleKernel(size):
    x = np.linspace(-1, 1, size)
    return x, [isocelesTriangle(x_i) for x_i in x]

def applyInterpolationKernel(x_p, y_p, kernelFunction):
    y_pp = np.zeros(len(y_p))

    # plot the convolutions, individually
    plt.figure()
    colors = ['r', 'g', 'm', 'y', 'b']
    for n in range(1, len(y)-1):
        _, kernel = kernelFunction(2*upsampling_factor+1)
        zeros = np.zeros(len(y_p))
        zeros[n*upsampling_factor] = y[n]
        convolution = np.convolve(zeros, kernel, 'same')
        y_pp += convolution
        plt.stem(x_p, convolution, colors[n%len(colors)], markerfmt=f'{colors[n%len(colors)]}o')

    # plot the sum of all convolutions
    plt.figure()
    plt.stem(x_p, y_pp,'r-')
    plt.stem(x_p, y_p)
    plt.legend(['Interpolated', 'Original'])

'''
Main
'''
applyInterpolationKernel(x_p, y_p, isocelesTriangleKernel)

import matplotlib.pylab as plt
from zeep import Client # SOAP client
import xml.etree.ElementTree as ET # read XMLs
import datetime
import os
import dateutil.parser

def plotLiborRate(liborRateScale: str, liborRateCode: int):
    dicc = client.service.ObtenerIndicadoresEconomicosXML(
        Indicador=liborRateCode, 
        FechaInicio=fechaInicio,
        FechaFinal=fechaFinal,
        Nombre = 'Juan M. Fonseca',
        SubNiveles = 'N',
        CorreoElectronico = 'juanma2268@gmail.com',
        Token = os.environ['BCCR_TOKEN']
    )
    
    # extract the XML that comes embedded in the dictionary data structure
    raiz = ET.fromstring(dicc)
    
    # build the signal
    x = []
    y = []
    for hijo in raiz:
        if 2<len(hijo):    # weekends have no rate
            x.append(dateutil.parser.isoparse(hijo[1].text))
            y.append(float(hijo[2].text))
        
    # plot
    return x, y

'''
Main
'''
client = Client('https://gee.bccr.fi.cr/Indicadores/Suscripciones/WS/wsindicadoreseconomicos.asmx?WSDL')

# Libor rates (https://gee.bccr.fi.cr/indicadoreseconomicos/Documentos/DocumentosMetodologiasNotasTecnicas/Webservices_de_indicadores_economicos.pdf)
liborRateScales = {
    '1': 349,
    '3': 350,
    '6': 351,
    '12': 352,
}

# find the Libor rate since a date in the past
fechaInicio = '01/01/2022'
fechaFinal = '16/07/2022'
liborRates = {}

plt.figure()
for liborRateScale in liborRateScales.keys():
    (dates, rates) = plotLiborRate(liborRateScale, liborRateScales[liborRateScale])
    print(f'Last {liborRateScale} month(s) Libor rates: {rates[-2:]}')
    liborRates[liborRateScale] = {'dates': dates, 'rates': rates}
    plt.plot(dates, rates)

plt.legend(liborRateScales.keys())
plt.xticks(rotation = 45)
plt.xlabel('Days')
plt.show()

Last 1 month(s) Libor rates: [2.156, 2.12029]
Last 3 month(s) Libor rates: [2.74029, 2.73757]
Last 6 month(s) Libor rates: [3.38129, 3.31129]
Last 12 month(s) Libor rates: [3.97829, 3.89643]

Interpolating the Libor rate¶

Summary¶

History¶

Interpolation kernels¶

References:¶

Notes¶

Appendix¶

Consuming the LIBOR rate from the BCCR SOAP web service¶