pycop 0.0.2

Copula and Tail Dependence Modelling

Copula and Tail Dependence

Install with

pip install pycop

Simple Usage

Import a sample

import pandas as pd
import numpy as np

df = pd.read_csv("data/msci1.csv")
df.index = pd.to_datetime(df["Date"], format='%m/%d/%Y')
df = df.drop(['Date'], axis=1)

for col in df.columns.values:
    df[col] = np.log(df[col]) - np.log(df[col].shift(1))

df = df.dropna()

Empirical Copula

from pycop.bivariate.copula import empirical

cop = Empirical(df[["US","UK"]])

Non-parametric Tail Dependence Coefficient

For a given threshold

cop.LTDC_(0.01) # i/n = 1%
cop.UTDC_(0.99) # i/n = 99%

Optimal Empirical Tail Dependence coefficient (TDC)

Returns optimal Empirical Tail Dependence coefficient (TDC) Based on the heuristic plateau-finding algorithm from Frahm et al (2005) "Estimating the tail-dependence coefficient: properties and pitfalls"

cop.optimal_tdc("upper") 
cop.optimal_tdc("lower")

Plot Copula density

Empirical

data = df[["Japan","US"]] cop = copula.Empirical(data) cop.plot_pdf(Nsplit=50)

Archimedean Copula

cop = copula.Archimedean(family='joe') param_, cmle = estimation.fit_cmle(cop, data) print(param_)

family1 = ['clayton', 'rgumbel','rjoe','rgalambos'] family2 = ['rclayton', 'gumbel','joe','galambos']

cop = copula.Mix2Copula(family1="clayton",family2="gumbel")

param_, cmle = estimation.fit_cmle(cop, data)

getting parameters

print(param_)

ltd = cop.LTD(w1=param_[0], theta1=param_[1]) utd = cop.UTD(w1=param_[0], theta2=param_[2])

print(ltd, utd)

Simulation

import matplotlib.pyplot as plt from bivariate import simulation

Gaussian Copula

u1, u2 = simulation.simu_gaussian(num=2000, rho=0.5) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()

Gaussian Copula with gaussian marginals

from scipy.stats import norm

u1, u2 = simulation.simu_gaussian(num=2000, rho=0.5) #apply distribution.ppf to transform uniform margin to the desired distribution in scipy.stats u1 = norm.ppf(u1) u2 = norm.ppf(u2) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()

Clayton

cop = copula.Archimedean(family='clayton') cop.plot_pdf(theta=1.5, Nsplit=25) cop.plot_cdf(theta=1.5, Nsplit=25)

Student Copula

u1, u2 = simulation.simu_tstudent(num=3000, nu=1, rho=0.5) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()

Clayton Copula

u1, u2 = simulation.simu_clayton(num=2000, theta=5) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()

Frank Copula

u1, u2 = simulation.simu_frank(num=2000, theta=5) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()

Gumbel Copula

u1, u2 = simulation.simu_gumbel(num=2000, theta=5) plt.scatter(u1, u2, color="black", alpha=0.8) plt.show()