R/put_price_concave.R

In mociepa/ShortfallRiskHedging: Shortfall Risk Hedging for european option

#' @title Calculate modified european put option
#'
#' @description
#' The put_price_concave function takes parameters from Black-Scholes model and returns a price of modified european put option.
#'
#' @usage put_price_concave(asset, strike, rate, vol, drift, p, time, End_Time, L, L2 = NA)
#'
#' @param asset a numeric vector of asset prices.
#' @param strike numeric value, strike price for call or put option.
#' @param rate numeric value, risk free rate in the model, r >= 0.
#' @param vol numeric value, volatility of the model, vol > 0.
#' @param drift numeric value, drift of the model.
#' @param time a numeric vector of actual time, time > 0.
#' @param p numeric positive value, power of the loss function, p < 1.
#' @param End_Time end time of the option, End_time >= time.
#' @param L numeric value, determines option payoff, L > 0.
#' @param L2 numeric value, determines option payoff, if L2 = NA, but is needed, function finds it with Newton's algorithm.
#' @return A numeric vector, price of the modification of european put option using concave loss function.
#'
#'
#' @examples
#' put_price_concave(100, 100, 0, 0.5, 0.05, 0.5,  0, 1, 80)
#' put_price_concave(c(100, 120), 100, 0, 0.3, 0.05, 0.5, 0, 1, 80)
#' put_price_concave(c(100, 120), 100, 0, 0.3, 0.05, 0.5, c(0, 0.5), 1, 60)
#'
#'
#'
#' @export

put_price_concave <- function(asset, strike, rate, vol, drift, p, time, End_Time, L, L2 = NA){
  if ( p <= 0 | p >= 1 ){
    stop("Wrong p argument. p is in the range (0, 1)")
  }

  m = drift - rate
  tau = End_Time - time

  if (length(tau) == 1){
    tau <- rep(tau, length(asset))
  }

  if (L >= strike){
    result <- 0
  }

  else{
    if (m >= 0){
      result1 <- put_price(asset, strike, rate, vol, time, End_Time) - put_price(asset, L, rate, vol, time, End_Time) +
        (L - strike)*exp(-rate*tau)*pnorm( -d2(asset, L, rate, vol, time, End_Time) )
      result <- ifelse(asset == L & tau == 0, 0, result1)
    }

    else{
      if (is.na(L2)){
        warning("In this case L2 is needed, while parameter L2 = NA. Calculated L2 argument by the Newton method (put_Newton_concave function).")
        L_bis <- put_Newton_concave(L, strike, drift, rate, vol, p)[1]
        L1 <- min(L, L_bis)
        L2 <- max(L, L_bis)
      }
      else{
        L1 <- min(L, L2)
        L2 <- max(L, L2)
      }

      result1 <- put_price(asset, strike, rate, vol, time, End_Time) - put_price(asset, L2, rate, vol, time, End_Time) +
        (L2 - strike)*exp(-rate*tau)*pnorm( -d2(asset, L2, rate, vol, time, End_Time) ) +
        put_price(asset, L1, rate, vol, time, End_Time) + (strike - L1)*exp(-rate*tau)*pnorm( -d2(asset, L1, rate, vol, time, End_Time) )
      result <- ifelse( ((asset == L1 | asset == L2) & tau == 0), 0, result1)
    }
  }
  return(result)
}