R/cf_lattice.R

In pedroguarderas/CFINI: Computational finance routines

# Multinomial lattice ------------------------------------------------------------------------------
#' @title Multinomial lattice
#' @description The option pricing can be made with a multinomial lattice, this functions can 
#' generate such a lattice with aid of some give parameters.
#' @param N number of periods for the multinomial model 
#' @param U vector of changes
#' @param S0 initial price
#' @return A list with a tree structure of the asset evolution
#' @author Pedro Guarderas
#' \email{pedro.felipe.guarderas@@gmail.com}
#' @examples
#' s <- 0.3
#' T <- 0.25
#' N <- 15
#' u <- exp( s * sqrt( T / N ) )
#' d <- 1/u
#' r <- 0.02
#' S0 <- 100
#' R <- exp( r * T / N )
#' q <- ( R - d ) / ( u - d )
#' U <- c( d, u )
#' S <- cf_lattice( N, U, S0 )
#' @export
cf_lattice <- function( N, U, S0 ) {
  S <- list( S0, U * S0 )
  n <- length( U )
  
  for ( t in 3:( N + 1 ) ) {
    M <- n + ( t - 2 ) * ( n - 1 )
    K <- M - n + 1
    S[[ t ]] <- c( U * S[[ t - 1 ]][ 1 ], U[ n ] * S[[ t - 1 ]][ 2:K ] )
  }
  return( new( 'cflattice', lattice = S, order = 2 ) )
}