R/call_Newton_convex.R

In mociepa/ShortfallRiskHedging: Shortfall Risk Hedging for european option

#' @title Finding constant in modified option.
#'
#' @description
#' The call_Newton_convex function is used to find second constant L in modified call option.
#'
#' @usage call_Newton_convex(L1, strike, drift, rate, vol, p, epsilon = 1e-10)
#'
#' @param L1 numeric value, first constant L1 > K.
#' @param strike numeric value, strike price for call option.
#' @param drift numeric value, drift of the model.
#' @param rate numeric value, risk free rate in the model, r >= 0.
#' @param vol numeric value, volatility of the model, vol > 0.
#' @param p numeric value, power of the loss function, p > 1.
#' @param epsilon numeric value, acceptable calculation error
#' @return A numeric value, a second constant for modified call option by convex function.
#'
#' @details There is a need to be careful when there is a warning message.
#' It means that a numerical error occurred during the algorithm and the algorithm was terminated without a while loop
#'
#' @examples
#' call_Newton_convex(140, 100, 0, 0.1, 0.2, 2)
#'
#' @export

call_Newton_convex <- function(L1, strike, drift, rate, vol, p, epsilon = 1e-10){
  if (p <= 1){
    stop("Wrong p argument. p > 1")
  }

  m = drift - rate
  k = -m / ( vol^2*(p - 1) )
  if(k <= 1){
    stop(paste("There is no need for a constant other than", L1))
  }

  c <- (L1 - strike) * L1^(-k)
  x_pocz <- ( 1 / (k*c) ) ^ ( 1 / (k - 1) )
  if(L1 <= x_pocz){
    x <- x_pocz + (x_pocz - L1) / 2
  }

  else{
    x =  strike
  }

  n = 0
  if( is.nan(c*x^(k) - x + strike) ){
    warning(paste("NaNs produced. Newton's algorithm was not fully working. Check if const are the same.", "For L1:",
                  call_const(L1, strike, drift, rate, vol, p), "For L2:",  call_const(x, strike, drift, rate, vol, p) ))
    return(x)
  }

  while ( abs( c*x^(k) - x + strike ) > epsilon ) {
    x <- x - (c * x^(k) - x + strike)/( k * c * x^(k-1) - 1 )
    n <- n + 1
  }

  return(x)
}