[Returnanalytics-commits] r3906 - pkg/Dowd/R

[noreply at r-forge.r-project.org]

Author: dacharya
Date: 2015-08-05 07:21:29 +0200 (Wed, 05 Aug 2015)
New Revision: 3906

Added:
   pkg/Dowd/R/AmericanPutESSim.R
Log:
Function AmericanPutESSim added

Added: pkg/Dowd/R/AmericanPutESSim.R
===================================================================
--- pkg/Dowd/R/AmericanPutESSim.R	                        (rev 0)
+++ pkg/Dowd/R/AmericanPutESSim.R	2015-08-05 05:21:29 UTC (rev 3906)
@@ -0,0 +1,84 @@
+#' Estimates ES of American vanilla put using binomial option valuation tree and Monte Carlo
+#' Simulation
+#' 
+#' Estimates ES of American Put Option using binomial tree to price the option
+#' valuation tree and Monte Carlo simulation with a binomial option valuation 
+#' tree nested within the MCS. Historical method to compute the VaR.
+#' 
+#' @param amountInvested Total amount paid for the Put Option and is positive 
+#' (negative) if the option position is long (short)
+#' @param stockPrice Stock price of underlying stock
+#' @param strike Strike price of the option
+#' @param r Risk-free rate
+#' @param mu Expected rate of return on the underlying asset and is in 
+#' annualised term
+#' @param sigma Volatility of the underlying stock and is in annualised 
+#' term
+#' @param maturity The term to maturity of the option in days
+#' @param numberTrials The number of interations in the Monte Carlo simulation
+#' exercise
+#' @param numberSteps The number of steps over the holding period at each
+#' of which early exercise is checked and is at least 2
+#' @param cl Confidence level for which VaR is computed and is scalar
+#' @param hp Holding period of the option in days and is scalar
+#' @return Monte Carlo Simulation VaR estimate and the bounds of the 95% 
+#' confidence interval for the VaR, based on an order-statistics analysis 
+#' of the P/L distribution
+#' @references Dowd, Kevin. Measuring Market Risk, Wiley, 2007.
+#' 
+#' Lyuu, Yuh-Dauh. Financial Engineering & Computation: Principles, 
+#' Mathematics, Algorithms, Cambridge University Press, 2002.
+#' 
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Market Risk of American Put with given parameters.
+#'    AmericanPutESSim(0.20, 27.2, 25, .16, .2, .05, 60, 30, 20, .95, 30)
+#'    
+#' @export
+AmericanPutESSim <- function(amountInvested, stockPrice, strike, r, mu, sigma, 
+                              maturity, numberTrials, numberSteps, cl, hp){
+  # Precompute Constants
+  annualMaturity <- maturity / 360 # Annualised maturity
+  annualHp <- hp / 360 # Annualised holding period
+  N <- numberSteps # Number of steps
+  dt <- annualHp / N # Size of time-increment equal to holding period
+  nudt <- (mu - .5 * sigma^2) * dt
+  sigmadt <- sigma * sqrt(dt)
+  lnS <- log(stockPrice)
+  M <- numberTrials
+  initialOptionPrice <- AmericanPutPriceBinomial(stockPrice, strike, r, sigma, maturity, N)
+  numberOfOptions <- abs(amountInvested) / initialOptionPrice
+  # Stock price simulation process
+  lnSt <- matrix(0, M, N)
+  newStockPrice <- matrix(0, M, N)
+  for (i in 1:M){
+    lnSt[i, 1] <- lnS + rnorm(1, nudt, sigmadt)
+    newStockPrice[i, 1] <- exp(lnSt[i, 1])
+    for (j in 2:N){
+      lnSt[i, j] <- lnSt[i, j - 1] + rnorm(1, nudt, sigmadt)
+      newStockPrice[i, j] <- exp(lnSt[i,j]) # New stock price
+    }
+  }
+  
+  # Option calculation over time
+  newOptionValue <- matrix(0, M, N-1)
+  for (i in 1:M) {
+    for (j in 1:(N-1)) {
+      newOptionValue[i, j] <- AmericanPutPriceBinomial(newStockPrice[i, j], 
+                                                       strike, r, sigma, maturity - j * hp / N, N)
+    }
+  }
+  # Profit/Loss
+  profitOrLoss <- (newOptionValue - initialOptionPrice)*numberOfOptions
+  
+  # Now adjust for short position
+  if (amountInvested < 0) {# If option position is short
+    profitOrLoss <- -profitOrLoss
+  }
+  
+  # VaR estimation
+  ES <- HSESDFPerc(profitOrLoss, .5, cl) # VaR
+  confidenceInterval <- c(HSESDFPerc(profitOrLoss, .025, cl), HSESDFPerc(profitOrLoss, .975, cl))
+  return(list('ES' = ES, 'confidenceInterval' = confidenceInterval))
+}
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