如何在R中绘制布朗运动(布莱克·斯科尔斯模拟)

install.packages(c("ggplot2", "reshape2", "animation"))
library(ggplot2)
library(reshape2)
library(animation)

brownian_motion <- function(n_steps, start_value = 0, volatility = 0.01) {
  steps <- rnorm(n_steps, mean = 0, sd = volatility)
  path <- cumsum(steps) + start_value
  return(path)
}

n_steps <- 1000
start_value <- 0
volatility <- 0.01

path <- brownian_motion(n_steps, start_value, volatility)

df <- data.frame(x = 1:n_steps, y = path)
ggplot(df, aes(x, y)) + geom_line() + labs(x = "步数", y = "路径值") + ggtitle("布朗运动路径图")

ani.options(interval = 0.1)
saveGIF({
  for (i in 1:n_steps) {
    df <- data.frame(x = 1:i, y = path[1:i])
    p <- ggplot(df, aes(x, y)) + geom_line() + labs(x = "步数", y = "路径值") + ggtitle("布朗运动路径图")
    print(p)
  }
}, movie.name = "brownian_motion.gif")