library(RandomWalk)
library(StockPriceSimulator)
library(ggplot2)
library(grid)
library(gridExtra)
## Call the path generating function from equation:
#
#
# Evolution of a Stock over 5 years. process track by
# formula and by ito.
stock_tick <- sstock(scale = 360, seed = 1, time_to_maturity = 5,
sigma = 1,
alpha = 0.12)
## Call the path generating function from Itôs approximation
stock_tick_ito <- sstock_ito(scale = 360, seed = 1, time_to_maturity = 5,
sigma = 1,
alpha = 0.12)
stock_tick_2 <- sstock(scale = 4, seed = 1, time_to_maturity = 5,
sigma = 1,
alpha = 0.12)
## Call the path generating function from Itôs approximation
stock_tick_ito_2 <- sstock_ito(scale = 4, seed = 1, time_to_maturity = 5,
sigma = 1,
alpha = 0.12)
stock_tick_3 <- sstock(scale = 360, seed = 1, time_to_maturity = 5,
sigma = .2,
alpha = 0.12)
## Call the path generating function from Itôs approximation
stock_tick_ito_3 <- sstock_ito(scale = 360, seed = 1, time_to_maturity = 5,
sigma = .2,
alpha = 0.12)
stock_tick_4 <- sstock(scale = 4, seed = 1, time_to_maturity = 5,
sigma = .2,
alpha = 0.12)
## Call the path generating function from Itôs approximation
stock_tick_ito_4 <- sstock_ito(scale = 4, seed = 1, time_to_maturity = 5,
sigma = .2,
alpha = 0.12)
p1 <- ggplot2::ggplot(stock_tick,
ggplot2::aes(time_periods, stock_price_path)) +
ggplot2::geom_line(color = 'pink') +
ggplot2::geom_line(data = stock_tick_ito,
ggplot2::aes(time_periods, stock_price_path),
color = 'steelblue')
p2 <- ggplot2::ggplot(stock_tick_2,
ggplot2::aes(time_periods, stock_price_path)) +
ggplot2::geom_line(color = 'pink') +
ggplot2::geom_line(data = stock_tick_ito_2,
ggplot2::aes(time_periods, stock_price_path),
color = 'steelblue')
p3 <- ggplot2::ggplot(stock_tick_3,
ggplot2::aes(time_periods, stock_price_path)) +
ggplot2::geom_line(color = 'pink') +
ggplot2::geom_line(data = stock_tick_ito_3,
ggplot2::aes(time_periods, stock_price_path),
color = 'steelblue')
p4 <- ggplot2::ggplot(stock_tick_4,
ggplot2::aes(time_periods, stock_price_path)) +
ggplot2::geom_line(color = 'pink') +
ggplot2::geom_line(data = stock_tick_ito_4,
ggplot2::aes(time_periods, stock_price_path),
color = 'steelblue')
grid.arrange(p1, p2, p3, p4, ncol = 2)
#
# Empicial distribution of Delta S / S
#
# stock_tick = vector(length = 3000)
# for(i in 1:3000)
# stock_tick[i] <- tail(sstock(scale = 360, seed = i, time_to_maturity = 5,
# sigma = .20,
# alpha = 0.12)$stock_price_path, 1)
#
# mean(stock_tick)
# 50 * exp(.12 * 5)
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