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############ Program: Simulation of copulas ###########
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# Author: Shengyu ZHENG (ESSEC Business School, Grande Ecole Program, Master in Management, 2020-2024)

# Version: 23/11/2023

# Objective of this file: To simulate 3 typical copulas 

# Structure of this file: 
#   I:  Prepration
#  II:  Simulation of a normal copula
# III:  Simulation of a Clayton copula (a type of Archimedean copula)
#  IV:  Simulation of a Tawn copula (a type of Extre Value copula)

# I: Prepration

if (!require(copula)) install.packages('copula')

library(copula)

n_samples <- 10000 # Number of simulated samples

# II: Simulation of normal copula

# Create a bivariate normal copula object with parameter being 0.8 
normal_copula <- normalCopula(0.8,dim = 2)

# Generate random samples from the copula
set.seed(100)
normal_copula_samples <- rCopula(n_samples, normal_copula)

# Plot the simulated data
plot(normal_copula_samples[, 1], normal_copula_samples[, 2], main = "Simulated Normal Copula", xlab = "U1", ylab = "U2")


# III:  Simulation of Clayton copula (a type of Archimedean copula)

# Create a Clayton copula object with parameter being 3
clayton_copula <- claytonCopula(3, dim = 2)

# Generate random samples from the copula
set.seed(101)
clayton_copula_samples <- rCopula(n_samples, clayton_copula)

# Plot the simulated data
plot(clayton_copula_samples[, 1], clayton_copula_samples[, 2], main = "Simulated Clayton Copula", xlab = "U1", ylab = "U2")


#  IV:  Simulation of a Tawn copula (a type of Extre Value copula)

# Create a Tawn copula object with parameter being 0.8
tawn_copula <- tawnCopula(param = 0.8)

# Generate random samples from the copula
set.seed(102)
tawn_copula_samples <- rCopula(n_samples, tawn_copula)

# Plot the simulated data
plot(tawn_copula_samples[, 1], tawn_copula_samples[, 2], main = "Simulated Tawn Copula", xlab = "U1", ylab = "U2")