R/myq_asian.R

In VarRedOpt: A Framework for Variance Reduction

#' @title Block Scholes for Geometric Asian Call Option
#'
#' @description Function to calculate expected value of Geometric Asian Call Option via Block Scholes formula.
#
#' @param zm Input matrix with n row and d dimension.
#' @param K Strike price.
#' @param ti Vector of control points.
#' @param r Riskfree rate.
#' @param sigma Yearly volatility.
#' @param S0 Stock price at start.
#'
#' @return Returns 4 elements as a list. Asian Call Option Prices, Last Price of Asian Call Option, Expected Value of Asian Call Option, Product of the prices through time
#'
#' @examples  sim.outer(n=1e3, d=3, q.outer = sim.IS,
#' q.is = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)
#' @export myq_asian
#' @export

myq_asian <- function(zm,K=100,ti=(1:3)/12,r=0.05,sigma=0.1,S0=100){
  # Simulation algorithm for Asian option
  # n... number of repetitions for the simulation
  # ti .. vector of control points. the last entry is the maturity T
  # Calculates expected value for the option
  # stores the last price is seperate variable named last_price
  # stores prdocuts of prices in a variable named prodSt

  # Returns:
  # ... last price , expected value, prodSt and Y in a list.

  d <- length(ti)
  dt <- ti[1]
  St <- S0*exp((r-sigma^2/2)*dt + sigma*sqrt(dt)*as.matrix(zm)[,1])
  sumSt <- St
  prodSt <- St
  # check if dimension is bigger than 1
  if(d>1){
    for(i in 2:d){
      dt <- ti[i] - ti[i-1]
      St <- St*exp((r-sigma^2/2)*dt + sigma*sqrt(dt)*zm[,i])
      sumSt <- sumSt + St
      prodSt <- prodSt * St
    }
  }
  # calculate asian option prices
  Y <- exp(-r*ti[d])* pmax(sumSt/d-K,0)
  # store the last price
  last_price <- St
  # calculate expected value
  E_z <- S0*exp(r*ti[d])
  # store them in a list
  returning_list = list(Y, last_price, E_z, prodSt)
  return(returning_list)
}