[Returnanalytics-commits] r3873 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-07-29 01:06:29 +0200 (Wed, 29 Jul 2015)
New Revision: 3873

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

Added: pkg/Dowd/R/AmericanPutPriceBinomial.R
===================================================================
--- pkg/Dowd/R/AmericanPutPriceBinomial.R	                        (rev 0)
+++ pkg/Dowd/R/AmericanPutPriceBinomial.R	2015-07-28 23:06:29 UTC (rev 3873)
@@ -0,0 +1,61 @@
+#' Binomial Put Price
+#' 
+#' Estimates the price of an American Put, using the binomial approach.
+#' 
+#' @param stockPrice Stock price of underlying stock
+#' @param strike Strike price of the option
+#' @param r Risk-free rate
+#' @param sigma Volatility of the underlying stock and is in annualised 
+#' term
+#' @param maturity The term to maturity of the option in days
+#' @param numberSteps The number of time-steps in the binomial tree
+#' @return Binomial American put price
+#' @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
+#' 
+#'    # Estimates the price of an American Put
+#'    AmericanPutPriceBinomial(27.2, 25, .03, .2, 60, 30)
+#'    
+#' @export
+AmericanPutPriceBinomial <- function(stockPrice, strike, r, sigma, 
+                             maturity, numberSteps){
+  prob <- .5 # Probability of up-move, equal probability approach used
+  N <- numberSteps
+  maturity <- maturity/360 # Convert maturity to units of years
+  deltat <- maturity/N # Length of incremental steps
+  u <- 2*exp(r * deltat + 2 * sigma * sqrt(deltat)) / (exp(2 * sigma * sqrt(deltat)) + 1) # Up-move
+  d <- 2*exp(r * deltat) / (exp(2 * sigma * sqrt(deltat)) + 1) # Dowd-move
+  # Note that there up- and down- moves incorporate risk  neutral approach
+  discount <- exp(-r * deltat) # Discount factor
+  # Stock price tree
+  S <- double(N+1)
+  S[1] <- stockPrice * (d ^ N)
+  for (i in 2:(N + 1)) { # i is number of up-moves plus 1
+    S[i] <- S[i-1] * u * u
+  }
+  # Option price tree
+  # Terminal option values
+  x <- double(N + 1)
+  for (i in 1:(N + 1)) {
+    x[i] <- max(strike - S[i], 0)
+  }
+  # Option values prior to expiration
+  for (j in seq(N, 1, -1)) {
+    for (i in 1:j){
+      x[i] <- discount * (prob * x[i + 1] + (1 - prob) * x[i])
+      S[i] <- S[i] * u
+      # Check for early exercise
+      exerciseValue <- max(0, strike - S[i])
+      if (exerciseValue > x[i]) {
+        x[i] <- exerciseValue
+      }
+    }
+  }
+  y <- x[1] # Initial option value
+  return(y)
+}
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