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alexchinco/plot--kyle-1989-model-solution--12nov2015.R

Created November 13, 2015 22:58
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Code to solve for the equilibrium parameters in the Kyle (1989) model
Raw
plot--kyle-1989-model-solution--12nov2015.R
## Prep workspace
options(width=120, digits=6, digits.secs=6)
rm(list=ls())
library(foreign)
library(grid)
library(plyr)
library(ggplot2)
library(tikzDevice)
print(options('tikzLatexPackages'))
options(tikzLatexPackages =
c("\\usepackage{tikz}\n",
"\\usepackage[active,tightpage,psfixbb]{preview}\n",
"\\PreviewEnvironment{pgfpicture}\n",
"\\setlength\\PreviewBorder{0pt}\n",
"\\usepackage{amsmath}\n",
"\\usepackage{pxfonts}\n",
"\\usepackage{bm}\n",
"\\usepackage{xfrac}\n"
)
)
setTikzDefaults(overwrite = FALSE)
print(options('tikzLatexPackages'))
library(reshape)
library(vars)
library(scales)
library(zoo)
library(splines)
library(MASS)
library(wmtsa)
library(foreach)
library(doMC)
registerDoMC(7)
## Define directories
scl.str.DAT_DIR <- "~/Dropbox/research/fast_trading_priced_noise/data/"
scl.str.FIG_DIR <- "~/Dropbox/research/fast_trading_priced_noise/figures/"
## Define global parameters
set.seed(123456)
scl.flt.RHO <- 1
scl.int.N <- 2
scl.int.M <- 1
scl.flt.TAU_E <- scl.int.N
scl.flt.TAU_V <- 1
vec.flt.TAU_Z <- seq(0.01, 2, by = 0.01)
## Define equlibrium functions
fun.VARPHI_I <- function(N, GAMMA_I, TAU_Z, TAU_E) {
OUT <- (N - 1) * GAMMA_I^2 / ((N - 1) * GAMMA_I^2 + TAU_E/TAU_Z)
return(OUT)
}
fun.VARPHI_U <- function(N, GAMMA_I, TAU_Z, TAU_E) {
OUT <- N * GAMMA_I^2 / (N * GAMMA_I^2 + TAU_E/TAU_Z)
return(OUT)
}
fun.TAU_I <- function(TAU_V, TAU_E, VARPHI_I, N) {
OUT <- TAU_V + TAU_E + VARPHI_I * (N - 1) * TAU_E
return(OUT)
}
fun.TAU_U <- function(TAU_V, TAU_E, VARPHI_U, N) {
OUT <- TAU_V + VARPHI_U * N * TAU_E
return(OUT)
}
## Define error functions
fun.OBJECTIVE <- function(ARGS, VAL) {
GAMMA_I <- ARGS[1]
ZETA <- ARGS[2]
XI_I <- ARGS[3]
XI_U <- ARGS[4]
RHO <- VAL[1]
TAU_V <- VAL[2]
TAU_Z <- VAL[3]
TAU_E <- VAL[4]
N <- VAL[5]
M <- VAL[6]
VARPHI_I <- fun.VARPHI_I(N, GAMMA_I, TAU_Z, TAU_E)
VARPHI_U <- fun.VARPHI_U(N, GAMMA_I, TAU_Z, TAU_E)
TAU_I <- fun.TAU_I(TAU_V, TAU_E, VARPHI_I, N)
TAU_U <- fun.TAU_U(TAU_V, TAU_E, VARPHI_U, N)
EQN1_ERR <- 1 - (N * XI_I + M * XI_U)
EQN2_ERR <- (1 - ZETA) - ((1 - VARPHI_I) * (1 - XI_I))
EQN3_ERR <- (RHO * GAMMA_I/TAU_E) - ((1 - VARPHI_I) * (1 - 2 * ZETA) / (1 - ZETA))
EQN4_ERR <- ((XI_U * ZETA * TAU_U/(1 - XI_U)) + (XI_U * RHO * GAMMA_I * TAU_I)/TAU_E) - (ZETA * TAU_U - VARPHI_U * TAU_I)
ERROR <- sum(c(EQN1_ERR^2, EQN2_ERR^2, EQN3_ERR^2, EQN4_ERR^2))
if (XI_I < VARPHI_U/N) {
ERROR <- ERROR + 100
}
if (XI_U > (1 - VARPHI_U)/M) {
ERROR <- ERROR + 100
}
LAM <- ZETA * TAU_E / (TAU_I * GAMMA_I)
if ((VARPHI_U * TAU_E) / (GAMMA_I * TAU_U * LAM) > 1) {
ERROR <- ERROR + 100
}
return(ERROR)
}
## Estimate equilibrium parameters
if (TRUE == TRUE) {
scl.int.TAU_Z_LEN <- length(vec.flt.TAU_Z)
mat.flt.COEF <- foreach(z=1:scl.int.TAU_Z_LEN, .combine = "rbind", .inorder = FALSE) %dopar% {
print(z)
vec.flt.VAL <- c(scl.flt.RHO,
scl.flt.TAU_V,
vec.flt.TAU_Z[z],
scl.flt.TAU_E,
scl.int.N,
scl.int.M
)
vec.flt.PAR <- c(1, 1/4, 1/6, 1/3)
obj.opt.OUT <- optim(par = vec.flt.PAR,
fn = fun.OBJECTIVE,
method = "L-BFGS-B",
lower = c(0, 0, 0, 0),
upper = c(Inf, 1/2, 1/scl.int.N, Inf),
VAL = vec.flt.VAL
)
vec.flt.OUT <- c(vec.flt.TAU_Z[z], obj.opt.OUT$par, obj.opt.OUT$value, obj.opt.OUT$convergence)
return(as.numeric(vec.flt.OUT))
}
mat.df.COEF <- as.data.frame(mat.flt.COEF)
names(mat.df.COEF) <- c("tauZ", "gamI", "zet", "xiI", "xiU", "err", "fit")
mat.df.COEF$varphiI <- fun.VARPHI_I(scl.int.N, mat.df.COEF$gamI, mat.df.COEF$tauZ, scl.flt.TAU_E)
mat.df.COEF$varphiU <- fun.VARPHI_U(scl.int.N, mat.df.COEF$gamI, mat.df.COEF$tauZ, scl.flt.TAU_E)
mat.df.COEF$tauI <- fun.TAU_I(scl.flt.TAU_V, scl.flt.TAU_E, mat.df.COEF$varphiI, scl.int.N)
mat.df.COEF$tauU <- fun.TAU_U(scl.flt.TAU_V, scl.flt.TAU_E, mat.df.COEF$varphiU, scl.int.N)
mat.df.COEF$lam <- mat.df.COEF$zet * scl.flt.TAU_E / (mat.df.COEF$tauI * mat.df.COEF$gamI)
mat.df.COEF$betI <- mat.df.COEF$xiI/mat.df.COEF$lam
mat.df.COEF$betU <- mat.df.COEF$xiU/mat.df.COEF$lam
mat.df.COEF$lamI <- 1/((scl.int.N - 1) * mat.df.COEF$betI + scl.int.M * mat.df.COEF$betU)
mat.df.COEF$lamU <- 1/(scl.int.N * mat.df.COEF$betI + (scl.int.M - 1) * mat.df.COEF$betU)
mat.df.COEF$muI <- 0
mat.df.COEF$muU <- 0
mat.df.COEF$tet <- (mat.df.COEF$varphiU * scl.flt.TAU_E) / (mat.df.COEF$gamI * mat.df.COEF$tauU * mat.df.COEF$lam)
save(mat.df.COEF, file = paste(scl.str.DAT_DIR, "data--kyle-1989-coef--12nov2015.Rdata"))
}
load(file = paste(scl.str.DAT_DIR, "data--kyle-1989-coef--12nov2015.Rdata"))
## Plot endogenous parameters
if (TRUE == TRUE) {
mat.df.PLOT <- mat.df.COEF[, c("tauZ", "gamI", "zet", "xiI", "xiU")]
names(mat.df.PLOT) <- c("tauZ",
"$\\gamma_I$",
"$\\zeta$",
"$\\xi_I$",
"$\\xi_U$"
)
mat.df.PLOT <- melt(mat.df.PLOT, c("tauZ"))
theme_set(theme_bw())
scl.str.RAW_FILE <- "plot--kyle-1989-model-solution--endogenous-param--12nov2015"
scl.str.TEX_FILE <- paste(scl.str.RAW_FILE,'.tex',sep='')
scl.str.PDF_FILE <- paste(scl.str.RAW_FILE,'.pdf',sep='')
scl.str.AUX_FILE <- paste(scl.str.RAW_FILE,'.aux',sep='')
scl.str.LOG_FILE <- paste(scl.str.RAW_FILE,'.log',sep='')
tikz(file = scl.str.TEX_FILE, height = 2.25, width = 7, standAlone=TRUE)
obj.gg2.PLOT <- ggplot()
obj.gg2.PLOT <- obj.gg2.PLOT + scale_colour_brewer(palette="Set1")
obj.gg2.PLOT <- obj.gg2.PLOT + geom_path(data = mat.df.PLOT,
aes(x = tauZ,
y = value
),
size = 1.25,
alpha = 0.50
)
obj.gg2.PLOT <- obj.gg2.PLOT + xlab("$\\tau_z$")
obj.gg2.PLOT <- obj.gg2.PLOT + ylab("")
obj.gg2.PLOT <- obj.gg2.PLOT + scale_x_continuous(limits = c(0, 2.0), breaks = c(0.00, 0.50, 1.00, 1.50, 2.00))
obj.gg2.PLOT <- obj.gg2.PLOT + facet_wrap(~ variable, nrow = 1, scales = "free_y")
obj.gg2.PLOT <- obj.gg2.PLOT + theme(plot.margin = unit(c(1,0.15,0.15,-1), "lines"),
axis.text = element_text(size = 8),
axis.title = element_text(size = 10),
plot.title = element_text(vjust = 1.75),
panel.grid.minor = element_blank(),
legend.position = "none"
)
obj.gg2.PLOT <- obj.gg2.PLOT + ggtitle("Endogenous Parameters")
print(obj.gg2.PLOT)
dev.off()
system(paste('lualatex', file.path(scl.str.TEX_FILE)), ignore.stdout = TRUE)
system(paste('rm ', scl.str.TEX_FILE, sep = ''))
system(paste('mv ', scl.str.PDF_FILE, ' ', scl.str.FIG_DIR, sep = ''))
system(paste('rm ', scl.str.AUX_FILE, sep = ''))
system(paste('rm ', scl.str.LOG_FILE, sep = ''))
}
## Plot price-impact coefficients
if (TRUE == TRUE) {
mat.df.PLOT <- mat.df.COEF[, c("tauZ", "lam", "lamI", "lamU", "tet")]
names(mat.df.PLOT) <- c("tauZ",
"$\\lambda$",
"$\\lambda_I$",
"$\\lambda_U$",
"$\\theta$"
)
mat.df.PLOT <- melt(mat.df.PLOT, c("tauZ"))
theme_set(theme_bw())
scl.str.RAW_FILE <- "plot--kyle-1989-model-solution--price-impact-coef--12nov2015"
scl.str.TEX_FILE <- paste(scl.str.RAW_FILE,'.tex',sep='')
scl.str.PDF_FILE <- paste(scl.str.RAW_FILE,'.pdf',sep='')
scl.str.AUX_FILE <- paste(scl.str.RAW_FILE,'.aux',sep='')
scl.str.LOG_FILE <- paste(scl.str.RAW_FILE,'.log',sep='')
tikz(file = scl.str.TEX_FILE, height = 2.25, width = 7, standAlone=TRUE)
obj.gg2.PLOT <- ggplot()
obj.gg2.PLOT <- obj.gg2.PLOT + scale_colour_brewer(palette="Set1")
obj.gg2.PLOT <- obj.gg2.PLOT + geom_path(data = mat.df.PLOT,
aes(x = tauZ,
y = value
),
size = 1.25,
alpha = 0.50
)
obj.gg2.PLOT <- obj.gg2.PLOT + xlab("$\\tau_z$")
obj.gg2.PLOT <- obj.gg2.PLOT + ylab("")
obj.gg2.PLOT <- obj.gg2.PLOT + scale_x_continuous(limits = c(0, 2.0), breaks = c(0.00, 0.50, 1.00, 1.50, 2.00))
obj.gg2.PLOT <- obj.gg2.PLOT + facet_wrap(~ variable, nrow = 1, scales = "free_y")
obj.gg2.PLOT <- obj.gg2.PLOT + theme(plot.margin = unit(c(1,0.15,0.15,-1), "lines"),
axis.text = element_text(size = 8),
axis.title = element_text(size = 10),
plot.title = element_text(vjust = 1.75),
panel.grid.minor = element_blank(),
legend.position = "none"
)
obj.gg2.PLOT <- obj.gg2.PLOT + ggtitle("Price-Impact Coefficients")
print(obj.gg2.PLOT)
dev.off()
system(paste('lualatex', file.path(scl.str.TEX_FILE)), ignore.stdout = TRUE)
system(paste('rm ', scl.str.TEX_FILE, sep = ''))
system(paste('mv ', scl.str.PDF_FILE, ' ', scl.str.FIG_DIR, sep = ''))
system(paste('rm ', scl.str.AUX_FILE, sep = ''))
system(paste('rm ', scl.str.LOG_FILE, sep = ''))
}
## Plot price-impact coefficients
if (TRUE == TRUE) {
mat.df.PLOT <- mat.df.COEF[, c("tauZ", "tauI", "tauU", "varphiI", "varphiU")]
names(mat.df.PLOT) <- c("tauZ",
"$\\tau_I$",
"$\\tau_U$",
"$\\varphi_I$",
"$\\varphi_U$"
)
mat.df.PLOT <- melt(mat.df.PLOT, c("tauZ"))
theme_set(theme_bw())
scl.str.RAW_FILE <- "plot--kyle-1989-model-solution--information-efficiency-parameters--12nov2015"
scl.str.TEX_FILE <- paste(scl.str.RAW_FILE,'.tex',sep='')
scl.str.PDF_FILE <- paste(scl.str.RAW_FILE,'.pdf',sep='')
scl.str.AUX_FILE <- paste(scl.str.RAW_FILE,'.aux',sep='')
scl.str.LOG_FILE <- paste(scl.str.RAW_FILE,'.log',sep='')
tikz(file = scl.str.TEX_FILE, height = 2.25, width = 7, standAlone=TRUE)
obj.gg2.PLOT <- ggplot()
obj.gg2.PLOT <- obj.gg2.PLOT + scale_colour_brewer(palette="Set1")
obj.gg2.PLOT <- obj.gg2.PLOT + geom_path(data = mat.df.PLOT,
aes(x = tauZ,
y = value
),
size = 1.25,
alpha = 0.50
)
obj.gg2.PLOT <- obj.gg2.PLOT + xlab("$\\tau_z$")
obj.gg2.PLOT <- obj.gg2.PLOT + ylab("")
obj.gg2.PLOT <- obj.gg2.PLOT + scale_x_continuous(limits = c(0, 2.0), breaks = c(0.00, 0.50, 1.00, 1.50, 2.00))
obj.gg2.PLOT <- obj.gg2.PLOT + facet_wrap(~ variable, nrow = 1, scales = "free_y")
obj.gg2.PLOT <- obj.gg2.PLOT + theme(plot.margin = unit(c(1,0.15,0.15,-1), "lines"),
axis.text = element_text(size = 8),
axis.title = element_text(size = 10),
plot.title = element_text(vjust = 1.75),
panel.grid.minor = element_blank(),
legend.position = "none"
)
obj.gg2.PLOT <- obj.gg2.PLOT + ggtitle("Information-Efficiency Parameters")
print(obj.gg2.PLOT)
dev.off()
system(paste('lualatex', file.path(scl.str.TEX_FILE)), ignore.stdout = TRUE)
system(paste('rm ', scl.str.TEX_FILE, sep = ''))
system(paste('mv ', scl.str.PDF_FILE, ' ', scl.str.FIG_DIR, sep = ''))
system(paste('rm ', scl.str.AUX_FILE, sep = ''))
system(paste('rm ', scl.str.LOG_FILE, sep = ''))
}
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