[Returnanalytics-commits] r2482 - pkg/Meucci/demo

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

Author: xavierv
Date: 2013-07-01 12:55:43 +0200 (Mon, 01 Jul 2013)
New Revision: 2482

Added:
   pkg/Meucci/demo/S_EquityProjectionPricing.R
Modified:
   pkg/Meucci/demo/S_EquitiesInvariance.R
Log:
added S_EquityProjectionPricing.R demo file

Modified: pkg/Meucci/demo/S_EquitiesInvariance.R
===================================================================
--- pkg/Meucci/demo/S_EquitiesInvariance.R	2013-07-01 08:26:27 UTC (rev 2481)
+++ pkg/Meucci/demo/S_EquitiesInvariance.R	2013-07-01 10:55:43 UTC (rev 2482)
@@ -1,7 +1,3 @@
-##################################################################################################################
-### This file performs the quest for invariance in the stock market
-### == Chapter 3 ==
-##################################################################################################################
 #' This file performs the quest for invariance in the stock market, as described in 
 #' A. Meucci "Risk and Asset Allocation", Springer, 2005, chapter 3.
 #'

Added: pkg/Meucci/demo/S_EquityProjectionPricing.R
===================================================================
--- pkg/Meucci/demo/S_EquityProjectionPricing.R	                        (rev 0)
+++ pkg/Meucci/demo/S_EquityProjectionPricing.R	2013-07-01 10:55:43 UTC (rev 2482)
@@ -0,0 +1,53 @@
+
+#' This script projects the distribution of the market invariants for the stock market (i.e. the compounded returns)
+#' from the estimation interval (normal assumption) to the investment horizon. Then it computes the distribution of prices
+#' at the investment horizon analytically, by full Monte Carlo, and by delta/duration approximationThis file performs 
+#' the quest for invariance in the stock market, as described in A. Meucci "Risk and Asset Allocation", Springer, 2005, 
+#' chapter 3.
+#'
+#' @references
+#' \url{http://symmys.com/node/170}
+#' See Meucci's script for "S_EquitiesInvariance.m"
+#'
+#' @author Xavier Valls \email{flamejat@@gmail.com}
+
+#################################################################################################################
+### Inputs
+tau_tilde = 1 / 52;  # estimation period expressed in years
+sig = 0.4;
+P_T = 1;
+NumScenarios = 1000000;
+taus    = c( 1/252, 1/52, 1/12, 1, 2 );    # times to horizon expressed in years
+tauName = c( '1 day','1 week', '1 month', '1 year', '2 years');
+
+#################################################################################################################
+### loop projection/pricing over different times to horizon
+for( k in 1 : length( taus ) )
+{ 
+    tau = taus[ k ];
+
+    # exact simulation of horizon prices
+    C_Ttau = rnorm( NumScenarios, 0, sqrt( sig * sig * tau));
+    P_Ttau = P_T * exp( C_Ttau );
+
+    # compute analytical pdf
+    p_lo = min( P_Ttau );
+    p_hi = max( P_Ttau );
+    p = seq( p_lo, p_hi, ( p_hi - p_lo ) / 1000 );
+    m = log( P_T );
+    s = sqrt( sig * sig * tau );
+    f = dlnorm( p, m, s );
+
+    # compute approximate pdf
+    f_approx = dnorm( p, P_T, sqrt(P_T * P_T * sig * sig * tau));
+
+    # plots
+    dev.new()
+    NumBins = round(10 * log( NumScenarios));
+    hist( P_Ttau, NumBins, freq = FALSE, xlab = "price at the horizon", ylab = "pdf", col="blue",
+     main = expression(paste("time to horizon ", tau, " = ", tauName[k])));
+    lines( p, f, col = "red");
+    lines( p, f_approx, col = "green");
+    legend( "topright", 1.9, c( "full Monte Carlo", "analytical", "delta/duration" ), col = c( "blue","red", "green" ),
+     lty=1,lwd =c( 10,1,1), bg = "gray90" );
+}
\ No newline at end of file