R/CRReuro.R

In RTL: Risk Tool Library - Trading, Risk, 'Analytics' for Commodities

#' Cox-Ross-Rubinstein binomial option model
#' @description
#' European option binomial model on a stock without dividends.For academic purpose only.
#' Use fOptions::CRRBinomialTreeOptions for real-life usage.
#' @param S Stock price. `numeric`
#' @param X Strike price. `numeric`
#' @param sigma Implied volatility e.g. 0.20 `numeric`
#' @param r Risk-free rate. `numeric`
#' @param T2M Time to maturity in years `numeric`
#' @param N Number of time steps. Internally dt = T2M/N. `numeric`
#' @param type "call" or "put" `character`
#' @returns List of asset price tree, option value tree and option price. `list`
#' @export CRReuro
#' @author Philippe Cote
#' @examples
#' CRReuro(S = 100, X = 100, sigma = 0.2, r = 0.1, T2M = 1, N = 5, type = "call")
CRReuro <- function(S, X, sigma, r, T2M, N, type) {
  dt <- T2M / N
  # Define u, d, and risk-neutral probability
  u <- exp(sigma * sqrt(dt))
  d <- exp(-sigma * sqrt(dt))
  q <- (exp(r * dt) - d) / (u - d)
  # Define our asset tree prices
  asset <- matrix(0, nrow = N + 1, ncol = N + 1)
  for (i in 1:(N + 1)) {
    for (j in 1:i) {
      asset[i, j] <- S * u^(j - 1) * d^((i - 1) - (j - 1))
    }
  }
  # create a matrix of the same dimensions as asset price tree
  option <- matrix(0, nrow = nrow(asset), ncol = ncol(asset))
  # replace last row with maturity payoffs
  if (type == "call") {
    option[nrow(option), ] <- pmax(asset[nrow(asset), ] - X, 0)
  }
  if (type == "put") {
    option[nrow(option), ] <- pmax(X - asset[nrow(asset), ], 0)
  }
  if (!type %in% c("call", "put")) stop("define option type: call or put")

  # we discount recursively starting from final payoff (last row of tree)
  # starting at the second last period based on final payoffs
  for (i in (nrow(option) - 1):1) {
    for (j in 1:i) {
      option[i, j] <- ((1 - q) * option[i + 1, j] + q * option[i + 1, j + 1]) / exp(r * dt)
    }
  }

  # indicator if model can be used sigma > rsqrt(dt)
  note <- if (sigma > sqrt(dt) * r) {
    "ok"
  } else {
    "sigma < rsqrt(dt) do not use"
  }

  return(list(asset = asset, option = option, price = option[1, 1], note = note))
}