Generates a binomial lattice for European option.

genlattice.european.R

# Generate a binomial lattice for European option.
genlattice.european <- function(Asset, Volatility, IntRate, DividendRate, Strike, Expiry, NoSteps, Payoff, Type) {
  
  # The number of tree nodes to process.
  count <- sum(1 : (NoSteps+1))
  
  # This data frame will store asset and option prices.
  # The mapping from tree node (i,j) to linear index
  # inside the data frame will have to be computed.
  X <- data.frame(matrix(NA, nrow=count, ncol=2))
  names(X) <- c("asset", "option")
  
  # Time between price movements.
  dt = Expiry / NoSteps
  
  # Option price discount factor.
  DiscountFactor <- exp(-IntRate * dt)
  
  # The up and down jump factors and
  # corresponding (synthetic) probabilities using 
  # Cox, Ross, and Rubinstein (1979) method.
  u = exp(Volatility * sqrt(dt))
  d = 1/u
  a = exp((IntRate - DividendRate) * dt)
  p = (a - d) / (u - d)
  
  # Compute the asset and option prices, starting 
  # from the last node of the tree, which is
  # its bottom right corner when viewed as a graph.
  # Work up and backwards. Backwards, comrades!
  for (i in NoSteps:0) {
    for (j in i:0) {
      X$asset[count] <- Asset * u^(i-j) * d^j
      
      # Compute the payoff directly for the last step's nodes,
      # otherwise use a formula.
      if (i == NoSteps) {
        X$option[count] <- Payoff(X$asset[count], Strike)
      } else {
        up   <- X$option[sum(1:(i+1), j, 1)]
        down <- X$option[sum(1:(i+1), j+1, 1)]
        X$option[count] <- DiscountFactor * (p * up + (1-p) * down)
      }
      
      count <- count - 1
    }
  }
  
  return(X)
}