app.R

# Required Packages
if (!require(shiny)) install.packages("shiny")
if (!require(ggplot2)) install.packages("ggplot2")

library(shiny)
library(ggplot2)

# Vectorized Black-Scholes Call Option Formula
bs_call_price_vec <- Vectorize(function(S, T, K, r, sigma){
  d1 <- (log(S/K) + (r + 0.5*sigma^2)*T) / (sigma*sqrt(T))
  d2 <- d1 - sigma*sqrt(T)
  S * pnorm(d1) - K * exp(-r*T) * pnorm(d2)
})

# UI
ui <- fluidPage(
  titlePanel("カーボンプライシング × ブラック＝ショールズモデル (Shiny版)"),
  
  sidebarLayout(
    sidebarPanel(
      numericInput("S0", "初期カーボン価格 ($/t-CO2)", value = 50, min = 1, max = 200),
      numericInput("mu", "ドリフト (期待成長率)", value = 0.05, step = 0.01),
      numericInput("sigma", "ボラティリティ", value = 0.2, step = 0.01),
      numericInput("K", "行使価格 ($)", value = 55, min = 1),
      numericInput("r", "無リスク金利", value = 0.01, step = 0.005),
      sliderInput("T", "満期 (年)", min = 0.1, max = 2, value = 1, step = 0.1),
      actionButton("simulate", "シミュレーション開始")
    ),
    
    mainPanel(
      plotOutput("carbonPlot"),
      plotOutput("optionPlot")
    )
  )
)

# Server
server <- function(input, output) {
  
  observeEvent(input$simulate, {
    set.seed(123)
    steps <- 252
    dt <- input$T / steps
    carbon_price <- numeric(steps + 1)
    carbon_price[1] <- input$S0
    
    for (i in 2:(steps + 1)) {
      carbon_price[i] <- carbon_price[i-1] * exp((input$mu - 0.5 * input$sigma^2) * dt + input$sigma * sqrt(dt) * rnorm(1))
    }
    
    time_to_maturity <- seq(input$T, 0, length.out = steps + 1)
    option_prices <- bs_call_price_vec(S = carbon_price, T = time_to_maturity, K = input$K, r = input$r, sigma = input$sigma)
    
    df <- data.frame(
      Day = 0:steps,
      CarbonPrice = carbon_price,
      OptionPrice = option_prices
    )
    
    output$carbonPlot <- renderPlot({
      ggplot(df, aes(x = Day, y = CarbonPrice)) +
        geom_line(color = "blue", size = 1) +
        labs(title = "Carbon Price Path",
             x = "Days",
             y = "Carbon Price ($/t-CO2)") +
        theme_minimal()
    })
    
    output$optionPlot <- renderPlot({
      ggplot(df, aes(x = Day, y = OptionPrice)) +
        geom_line(color = "darkgreen", size = 1) +
        labs(title = "European Call Option Price",
             x = "Days",
             y = "Option Price ($)") +
        theme_minimal()
    })
  })
  
}

# Run App
shinyApp(ui = ui, server = server)