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simple_market_model.R
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simple_market_model.R
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#####################################################################################################
## See accompanying blog post: ##
## https://blog.ephorie.de/can-a-simple-multi-agent-model-replicate-complex-stock-market-behaviour ##
#####################################################################################################
# For reproducibility
set.seed(2718)
# Initialize no. of trading days (5000 days -> about 20 years)
N <- 5000
# Initialize no. of traders
trader_count <- 500
traders <- data.frame(
indicator = rep(1, trader_count),
behavior = runif(trader_count), # Random uniform values between 0 and 1
color = rep(NA, trader_count)
)
# Set behavior and color based on random value
traders$behavior <- ifelse(traders$behavior < 0.5, 0, 1)
traders$color <- ifelse(traders$behavior == 0, "black", "yellow")
# Define global variables
global_vars <- list("log_price" = 0,
"last_price" = 0,
"return" = 0,
"F" = 0,
"orders_by_technical_rules" = 0,
"orders_by_fundamental_rules" = 0,
"orders_by_technical_rules2" = 0,
"orders_by_fundamental_rules2" = 0,
"orders_by_technical_rules3" = 0,
"orders_by_fundamental_rules3" = 0,
"weight_technical_traders" = 0,
"weight_fundamental_traders" = 0,
"fitness_technical_rules" = 0,
"fitness_fundamental_rules" = 0,
"fitness_technical_rules2" = 0,
"fitness_fundamental_rules2" = 0,
"K" = sum(traders$indicator[traders$behavior == 1]),
"K2" = 0,
"N" = sum(traders$indicator),
"alpha" = 0,
"beta" = 0,
"gamma" = 0,
"agent2_behavior" = 0,
"talks_done" = 0,
"probab_change_tech_fund" = 0,
"probab_change_fund_tech" = 0,
"transition_prob_tech_plus" = 0,
"transition_prob_tech_minus" = 0,
"transition_prob" = 0,
"random_no" = 0,
"a" = 1,
"b" = 0.05,
"c" = 0.02,
"d" = 0.95,
"epsilon" = 0.10,
"lambda" = 0.45,
"sigma_alfa" = 0.0025,
"sigma_beta" = 0.025,
"sigma_gamma" = 0.0025,
"talks_total" = 20)
# Define performance metrics
performance <- list("returns" = c(),
"log_prices" = c(),
"weights_technical_traders" = c())
# Define function for agent interaction
agent_talk_and_decision <- function(traders, global_vars) {
talks_done <- 0
while (global_vars$talks_total >= talks_done) {
random_no <- runif(1, 0, 1)
if (random_no < global_vars$transition_prob) {
talks_done <- talks_done + 1
} else {
if (random_no >= global_vars$transition_prob && random_no < (global_vars$transition_prob + global_vars$transition_prob_tech_plus)) {
patch_to_change <- sample(which(traders$behavior == 0), 1)
traders$behavior[patch_to_change] <- 1
traders$color[patch_to_change] <- "yellow"
talks_done <- talks_done + 1
} else {
patch_to_change <- sample(which(traders$behavior == 1), 1)
traders$behavior[patch_to_change] <- 0
traders$color[patch_to_change] <- "black"
talks_done <- talks_done + 1
}
}
}
list(traders = traders, global_vars = global_vars)
}
# Define function for market mechanism
market_clearing <- function(traders, global_vars) {
global_vars$alpha <- rnorm(1, 0, global_vars$sigma_alfa)
global_vars$beta <- rnorm(1, 0, global_vars$sigma_beta)
global_vars$gamma <- rnorm(1, 0, global_vars$sigma_gamma)
# updating order variables
global_vars$orders_by_technical_rules3 <- global_vars$orders_by_technical_rules2
global_vars$orders_by_technical_rules2 <- global_vars$orders_by_technical_rules
global_vars$orders_by_technical_rules <- global_vars$b * (global_vars$log_price - global_vars$last_price) + global_vars$beta
global_vars$orders_by_fundamental_rules3 <- global_vars$orders_by_fundamental_rules2
global_vars$orders_by_fundamental_rules2 <- global_vars$orders_by_fundamental_rules
global_vars$orders_by_fundamental_rules <- global_vars$c * (global_vars$F - global_vars$log_price) + global_vars$gamma
# updating weights
global_vars$K2 <- global_vars$K
global_vars$K <- sum(traders$indicator[traders$behavior == 1])
global_vars$weight_technical_traders <- global_vars$K / global_vars$N
global_vars$weight_fundamental_traders <- (global_vars$N - global_vars$K) / global_vars$N
# updating price
global_vars$last_price <- global_vars$log_price
global_vars$log_price <- global_vars$last_price + global_vars$a * (global_vars$orders_by_technical_rules * global_vars$weight_technical_traders +
global_vars$orders_by_fundamental_rules * global_vars$weight_fundamental_traders) + global_vars$alpha
# calculating return
if (global_vars$last_price == 0) {
global_vars$return <- 0.0
} else {
global_vars$return <- global_vars$log_price - global_vars$last_price
}
# fitness rule calculations
global_vars$fitness_technical_rules2 <- global_vars$fitness_technical_rules
global_vars$fitness_fundamental_rules2 <- global_vars$fitness_fundamental_rules
global_vars$fitness_technical_rules <- ((exp(global_vars$log_price) - exp(global_vars$last_price)) * global_vars$orders_by_technical_rules3 + global_vars$d * global_vars$fitness_technical_rules2)
global_vars$fitness_fundamental_rules <- ((exp(global_vars$log_price) - exp(global_vars$last_price)) * global_vars$orders_by_fundamental_rules3 + global_vars$d * global_vars$fitness_fundamental_rules2)
# probabilities that agents change their opinion and use different rules
if (global_vars$fitness_technical_rules > global_vars$fitness_fundamental_rules) {
global_vars$probab_change_fund_tech <- (0.5 + global_vars$lambda)
global_vars$probab_change_tech_fund <- (0.5 - global_vars$lambda)
} else {
global_vars$probab_change_fund_tech <- (0.5 - global_vars$lambda)
global_vars$probab_change_tech_fund <- (0.5 + global_vars$lambda)
}
# transition probabilities
global_vars$transition_prob_tech_plus <- ((global_vars$N - global_vars$K2) / global_vars$N) * (global_vars$epsilon + global_vars$probab_change_fund_tech * (global_vars$K2 / (global_vars$N - 1)))
global_vars$transition_prob_tech_minus <- (global_vars$K2 / global_vars$N) * (global_vars$epsilon + global_vars$probab_change_tech_fund * ((global_vars$N - global_vars$K2) / (global_vars$N - 1)))
global_vars$transition_prob <- 1 - global_vars$transition_prob_tech_plus - global_vars$transition_prob_tech_minus
list(traders = traders, global_vars = global_vars)
}
# Define function for storing performance metrics
do_report <- function(global_vars, performance) {
performance$returns <- c(performance$returns, global_vars$return)
performance$log_prices <- c(performance$log_prices, global_vars$log_price)
performance$weights_technical_traders <- c(performance$weights_technical_traders, global_vars$weight_technical_traders)
performance
}
# Run the simulation
start.time <- Sys.time()
for(ticks in 1:N) {
if (ticks > 2) {
results <- agent_talk_and_decision(traders, global_vars)
traders <- results$traders
global_vars <- results$global_vars
}
results <- market_clearing(traders, global_vars)
traders <- results$traders
global_vars <- results$global_vars
performance <- do_report(global_vars, performance)
}
Sys.time() - start.time
returns <- performance$returns[-1]
logprices <- performance$log_prices
weights <- performance$weights_technical_traders
# Plot results
library(forecast)
library(laeken)
tailindex <- function(data) {
len <- length(data)
pc <- seq(5, len/10, 5)
plot_data <- sapply(pc, thetaHill, x = data)
plot(plot_data,type = "l", main = "", ylab = "tail index", xlab = "largest observations", xaxt = "n")
axis(1, at = c(0, length(plot_data)/2, length(plot_data)), labels = c(0, 5, 10))
paste("Tailindex at 5%:", round(thetaHill(data, len/20), 1))
}
plot(logprices, ylab = "log price", xlab = "time", type = "l")
abline(h = 0)
plot(returns, ylab = "return", xlab = "time", type = "l")
abline(h = 0)
plot(weights, ylab = "weights", xlab = "time", type = "l")
abline(h = 0.5)
plot(density(returns), main = "", ylab = "prob frequency", xlab = "return")
curve(dnorm(x, mean(returns), sd(returns)), col = "red", add = TRUE)
tailindex(abs(returns))
Acf(returns, lag.max = 100, main = "", ylab = "acf r", xlab = "lag")
Acf(abs(returns), lag.max = 100, main = "", ylab = "acf |r|", xlab = "lag")