[Returnanalytics-commits] r3887 - pkg/Dowd/R

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

Author: dacharya
Date: 2015-07-31 11:23:53 +0200 (Fri, 31 Jul 2015)
New Revision: 3887

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

Added: pkg/Dowd/R/LongBlackScholesCallVaR.R
===================================================================
--- pkg/Dowd/R/LongBlackScholesCallVaR.R	                        (rev 0)
+++ pkg/Dowd/R/LongBlackScholesCallVaR.R	2015-07-31 09:23:53 UTC (rev 3887)
@@ -0,0 +1,42 @@
+#' Derives VaR of a long Black Scholes call option
+#' 
+#' Function derives the VaR of a long Black Scholes call for specified 
+#' confidence level and holding period, using analytical solution.
+#' 
+#' @param stockPrice Stock price of underlying stock
+#' @param strike Strike price of the option
+#' @param r Risk-free rate and is annualised
+#' @param mu Mean return
+#' @param sigma Volatility of the underlying stock
+#' @param maturity Term to maturity and is expressed in days
+#' @param cl Confidence level and is scalar
+#' @param hp Holding period and is scalar and is expressed in days
+#' @return Price of European Call Option
+#' @references Dowd, Kevin. Measuring Market Risk, Wiley, 2007.
+#' 
+#' Hull, John C.. Options, Futures, and Other Derivatives. 4th ed., Upper Saddle
+#' River, NJ: Prentice Hall, 200, ch. 11.
+#' 
+#' Lyuu, Yuh-Dauh. Financial Engineering & Computation: Principles, 
+#' Mathematics, Algorithms, Cambridge University Press, 2002.
+#' 
+#' @author Dinesh Acharya
+#' @examples
+#' 
+#'    # Estimates the price of an American Put
+#'    LongBlackScholesCallVaR(27.2, 25, .03, .12, .2, 60, .95, 40)
+#'    
+#' @export
+LongBlackScholesCallVaR <- function(stockPrice, strike, r, mu, sigma, 
+                                    maturity, cl, hp){
+  # Simplify notation
+  t <- maturity/360
+  hp <- hp/360
+  currentOptionPrice <- BlackScholesCallPrice(stockPrice, strike, r, sigma, t)
+  sStar <- exp(log(stockPrice) + (mu - (sigma ^ 2)/2) * hp - 
+                 qnorm(cl, 0, 1) * sigma * sqrt(hp))
+  # Critical future stock price, see Hull, p. 238
+  futureOptionPriceStar <- BlackScholesCallPrice(sStar, strike, r, sigma, t - hp)
+  y <- currentOptionPrice - futureOptionPriceStar
+  return(y)
+}
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