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Classical_EPK_SP500.R
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Classical_EPK_SP500.R
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# Clear variables and close windows
rm(list = ls(all = TRUE))
graphics.off()
# Set working directory
# setwd('~/...') # linux/mac os
# setwd('/Users/...') # windows
## Install packages
# install.packages(KernSmooth)
# install.packages(rugarch)
# install.packages(fGarch)
# install.packages(forecast)
# install.packages(TSA)
# install.packages(ks)
# install.packages(matlab)
# install.packages("optimx")
# Load packages
library(KernSmooth)
library(rugarch)
# library(fGarch)
library(forecast)
library(TSA)
library(ks)
library(matlab)
library(splines) # bs()
library(pracma)
library(optimx)
library(data.table)
library(dplyr)
library(ggplot2)
library(dplyr)
library(readxl)
# set directory
# path <- "~/Library/CloudStorage/OneDrive-NationalUniversityofSingapore/PAPER/Pricing/code/test/"
Path_raw = "/Users/ruting/Library/Mobile Documents/com~apple~CloudDocs/PK_BTC/code_data/"
path <- "/Users/ruting/Library/Mobile Documents/com~apple~CloudDocs/PK_BTC/code_data/main_code/"
setwd(path)
path_Qfile <- paste0(path,"Q_density_files_SP500/")
directories <- list.files(path = path_Qfile, full.names = FALSE, recursive = FALSE)
# classical part
HDEgarch = function(garchfit, data, grid, maturity, N, start){
# Simulation
garchsim = ugarchsim(garchfit, n.sim = round(maturity),
n.start = 0, m.sim=N, startMethod=("sample"),
mexsimdata=TRUE)
# head(g11sim@simulation)[2]= extracting simulated return data
returnsim = as.vector(head(garchsim@simulation)[2])
# Calculating spot prices from return data
value = matrix(0,ncol=5000)
for(i in 1:N) {
value[,i] = start*exp(sum(returnsim$seriesSim[,i]))
}
# Computing density on given grid: Either by using build in function (kde(...)):
# kde() computes bandwith h wih function hpi() which uses Wand&Jones (1994) estimator
# grid: strike
ValDens = kde(value[1,],eval.points=grid, gridsize=length(grid),
xmin=min(grid), xmax=max(grid))
return(ValDens$estimate)
}
Price_infor = read.csv(paste0(Path_raw,'SP500_data/sp500_price_daily.csv'))%>% data.frame()
sp1 <- Price_infor
# sp1 <- sp1[!(as.Date(sp1$Date) < as.Date(dates_Q[i]) | as.Date(sp1$Date) > as.Date(dates_Q[i]) + tau), ]
sp1.retts = ts(log(sp1$Close)[2:nrow(sp1)]-log(sp1$Close)[1:(nrow(sp1)-1)])
# rt <- seq(-1, log(sp1$Adj.Close[nrow(sp1)] / sp1$Adj.Close[1]), length.out = 500)
# Parameters for calculation/simulation
numbapprox = 2000 # fineness of the grid
N = 5000 # No. of Simulations
# Check return series for ARMA effects, e.g. with the following function
# auto.arima(dax.retts, max.p=10, max.q=10, max.P=5, max.Q=5,
# start.p=1, start.q=1,start.P=1, start.Q=1, stationary=T, seasonal=F)
p = 0
q = 0
arma = c(p,q)
# specify garch order (need to be checked)
m = 1
s = 1
garch = c(m,s)
# Specify GARCH model (default is standard GARCH)
# for changing GARCH-model + submodel, please refer to
# rugarch package for further information
garchmodel = "fGARCH"
submodel = "GARCH"
# underlying distribution (default: "sstd" - skewed stundent t's)
# (alternatives: "norm" - normal, "ghyp"- generalized hyperbolic)
udist = "sstd"
# set archm=T for ARCH in mean model (archpow specifies the power)
archm = F
archpow = 1
# set include.mean = F if you don't want to include a mean in the mean model
include.mean = T
spec = ugarchspec(variance.model = list(model = garchmodel,
garchOrder = garch, submodel = submodel), mean.model =
list(armaOrder = arma, archm=archm,archpow=archpow,
include.mean=include.mean), distribution.model = udist)
dir.create(paste0(path,"EPKPlot_SP500"), showWarnings = FALSE)
# 4y 6y 8y 10y
rolling = c(4, 6, 8, 10)
rolling = 4
# tau = 30
# tau_files <- grep( paste0("raw_Q_density.*tau",tau,"\\.csv$"), directories, value = TRUE)
# dates <- gsub("raw_Q_density_([0-9]{4}-[0-9]{2}-[0-9]{2})_tau.*", "\\1", tau_files)
# dates_Q <- dates[1:(length(dates) - 1)]
date_tau = read_excel('SP500_Classic_date.xlsx')
date_tau$dates_Q = as.character(date_tau$dates_Q )
for (i in c(1:nrow(date_tau))){
setwd(paste0(path, 'Q_density_files_SP500'))
tau = date_tau$tau[i]
figure_save = paste0(path,"EPKPlot_SP500/tau_",tau)
dir.create(figure_save, showWarnings = FALSE)
a <- paste0(path_Qfile,"raw_Q_density_", date_tau$dates_Q[i], "_tau", date_tau$tau[i], ".csv")
# 检查文件是否存在
if (!file.exists(a)) {
print(paste("no files for", date_tau$dates_Q[i], "tau", date_tau$tau[i]))
next # 如果文件不存在，跳过这个循环
}
data_q = read.csv(a)
data_q = data_q[order(data_q$m),]
data_q$Strike = data_q$x
data_q$Q_density = data_q$y
SpotPrice = mean(data_q$Strike * data_q$m)
# data_q$Q_density = data_q$y
# sp1_h <- sp1[as.Date(sp1$Date) < as.Date(dates_Q[i]), ]
for (iRoll in rolling){
sp1_h <- sp1[as.Date(sp1$Date) < as.Date(date_tau$dates_Q[i]), ]
sp1_h <- sp1[(nrow(sp1_h)-iRoll*360):nrow(sp1_h),]
sp1.retts = ts(log(sp1_h$Close)[2:nrow(sp1_h)]-log(sp1_h$Close)[1:(nrow(sp1_h)-1)])
garchfit = ugarchfit(data=sp1.retts, spec=spec, solver = "hybrid")
HDE = HDEgarch(garchfit, sp1.retts, data_q$Strike,
tau, N =5000, SpotPrice)
EPK = data.frame(M = data_q$m,EPK = data_q$Q_density / HDE, Q = data_q$Q_density, P = HDE,Strike = data_q$Strike )
EPK = EPK[EPK$EPK>0&EPK$M<1.07&EPK$M>0.93,]
# Save the plot to a PNG file
png(paste0(figure_save, "/SP500_", date_tau$dates_Q[i], "_tau_", tau, "_", iRoll, "YearRoll_Classical.png"), width = 800, height = 600, bg = "transparent")
# Ensure there are no missing or infinite values in EPK$M and EPK$EPK
EPK <- EPK[!is.na(EPK$M) & !is.na(EPK$EPK) & !is.infinite(EPK$M) & !is.infinite(EPK$EPK), ]
# Check if the data frame is not empty after removing NA and Inf values
if (nrow(EPK) > 0) {
# Calculate xlim and ylim ensuring finite values
xlim_vals <- range(EPK$M, na.rm = TRUE, finite = TRUE)
ylim_vals <- quantile(EPK$EPK, probs = c(0.05, 0.95), na.rm = TRUE, finite = TRUE)
# Debugging: Print the calculated xlim and ylim values
print(paste("xlim:", xlim_vals))
print(paste("ylim:", ylim_vals))
# Plot only if xlim and ylim values are finite
if (all(is.finite(xlim_vals)) && all(is.finite(ylim_vals))) {
plot(EPK$M, EPK$EPK, type = 'l', col = 'black', lwd = 2,
xlab = "Moneyness", ylab = "EPK",
cex.lab = 1.25, # 坐标轴标签字体大小
cex.axis = 1.25,
xlim = xlim_vals, ylim = ylim_vals, # x 和 y 轴的范围
cex.main = 1.25)
} else {
warning("Non-finite xlim or ylim values, plot not created.")
}
} else {
warning("Data frame is empty after removing NA and Inf values, plot not created.")
}
# Close the graphics device
dev.off()
# plot(EPK$Strike, EPK$Q, type = 'l', col = 'red',
# xlab = "Strike", ylab = "Q density",
# xlim = c(min(EPK$Strike), max(EPK$Strike)), ylim = c(quantile(EPK$Q, probs = c(0.01)),quantile(EPK$Q, probs = c(0.99))),
# main = paste(dates_Q[i], "Q density")
# )
# lines(EPK$Strike, EPK$P, col = 'blue')
#
#
# plot(EPK$Strike, EPK$P, type = 'l', col = 'black',
# xlab = "Strike", ylab = "P density",
# xlim = c(min(EPK$Strike), max(EPK$Strike)), ylim = c(quantile(EPK$P, probs = c(0.01)),quantile(EPK$P, probs = c(0.99))),
# main = paste(dates_Q[i], "Classical EPK")
# )
#
Plot_Out = data.frame(x = rep(EPK$M,2), density = c(EPK$Q,EPK$P), line = factor(rep(c("Q_density","P_density"), each = nrow(EPK))))
my_plot <-ggplot(Plot_Out, aes(x = x, y = density, color = line)) +
geom_line(size = 1) +
labs(x=NULL,y = "Density")+
theme(legend.key = element_rect(fill = "transparent"),
axis.ticks.length = unit(-0.2, "cm"),
panel.grid = element_blank(),
axis.line = element_line(color = "black", linewidth = 0.5),
plot.background = element_rect(fill = "transparent"),
legend.background = element_rect(fill = "transparent"), # Set legend background to transparent
panel.background = element_rect(fill = "transparent"),
)
plot(my_plot)
ggsave(paste0(figure_save,"/SP500_Density_",date_tau$dates_Q[i],"_tau_",tau,"_",iRoll,"YearRoll.png"), my_plot, width = 3200, height = 1600, units = "px")
}
}
for (i in c(1:length(dates_Q))) {
setwd(paste0(path, 'Q_density_files_SP500'))
a <- paste0(path_Qfile,"raw_Q_density_", dates_Q[i], "_tau", tau, ".csv")
# 检查文件是否存在
if (!file.exists(a)) {
print(paste("no files for", dates_Q[i], "tau", tau))
next # 如果文件不存在，跳过这个循环
}
data_q = read.csv(a)
data_q = data_q[order(data_q$m),]
data_q$Strike = data_q$x
data_q$Q_density = data_q$y
SpotPrice = mean(data_q$Strike * data_q$m)
# data_q$Q_density = data_q$y
# sp1_h <- sp1[as.Date(sp1$Date) < as.Date(dates_Q[i]), ]
sp1_h <- sp1_h[(nrow(sp1_h)-4*360):nrow(sp1_h),]
sp1.retts = ts(log(sp1_h$Close)[2:nrow(sp1_h)]-log(sp1_h$Close)[1:(nrow(sp1_h)-1)])
garchfit = ugarchfit(data=sp1.retts, spec=spec, solver = "hybrid")
HDE = HDEgarch(garchfit, sp1.retts, data_q$Strike,
tau, N = length(data_q$Strike), SpotPrice)
EPK = data.frame(M = data_q$m,EPK = data_q$Q_density / HDE, Q = data_q$Q_density, P = HDE,Strike = data_q$Strike )
EPK = EPK[EPK$EPK>0&EPK$M<1.05&EPK$M>0.93,]
png(paste0(figure_save,"/SP500_",dates_Q[i],"_tau_",tau,"_Classical.png"), width = 800, height = 600, bg = "transparent")
plot(EPK$M, EPK$EPK, type = 'l', col = 'black',
xlab = "Moneyness", ylab = "EPK",
xlim = c(min(EPK$M), max(EPK$M)), ylim = c(quantile(EPK$EPK, probs = c(0.05)),quantile(EPK$EPK, probs = c(0.95))),
main = paste(dates_Q[i], "Classical EPK")
)
dev.off()
# plot(EPK$Strike, EPK$Q, type = 'l', col = 'red',
# xlab = "Strike", ylab = "Q density",
# xlim = c(min(EPK$Strike), max(EPK$Strike)), ylim = c(quantile(EPK$Q, probs = c(0.01)),quantile(EPK$Q, probs = c(0.99))),
# main = paste(dates_Q[i], "Q density")
# )
# lines(EPK$Strike, EPK$P, col = 'blue')
#
#
# plot(EPK$Strike, EPK$P, type = 'l', col = 'black',
# xlab = "Strike", ylab = "P density",
# xlim = c(min(EPK$Strike), max(EPK$Strike)), ylim = c(quantile(EPK$P, probs = c(0.01)),quantile(EPK$P, probs = c(0.99))),
# main = paste(dates_Q[i], "Classical EPK")
# )
#
Plot_Out = data.frame(x = rep(EPK$M,2), density = c(EPK$Q,EPK$P), line = factor(rep(c("Q_density","P_density"), each = nrow(EPK))))
my_plot <-ggplot(Plot_Out, aes(x = x, y = density, color = line)) +
geom_line(size = 1) +
labs(x=NULL,y = "Density")+
theme(legend.key = element_rect(fill = "transparent"),
axis.ticks.length = unit(-0.2, "cm"),
panel.grid = element_blank(),
axis.line = element_line(color = "black", linewidth = 0.5),
plot.background = element_rect(fill = "transparent"),
legend.background = element_rect(fill = "transparent"), # Set legend background to transparent
panel.background = element_rect(fill = "transparent"),
)
plot(my_plot)
ggsave(paste0(figure_save,"/SP500_Density_",dates_Q[i],"_tau_",tau,".png"), my_plot, width = 3200, height = 1600, units = "px")
}