first commit

Author: romanlykhnenko

NIC_Lykhnenko_Roman.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

class_compound_poisson.R

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+source("required_libraries.R")
+
+#
+# constructor of the class compoundPoisson -------------------------------------
+#
+compoundPoisson <-function(drift, jumpIntensity){
+  
+  # drift parameter
+  b = drift
+  
+  # jump parameter
+  lamda = jumpIntensity
+  
+  # simulation of the process on the the interval [0,T]
+  T  = 1
+  
+  # at these points value of the process is due to be calculated
+  t     = seq(0, T, by = 0.00001)
+  
+  # simulate a r.v. N from Poisson distribution with parameter lamda*T.
+  # N gives the total number of jumps on the interval [0, T]
+  N = rpois(1,lamda*T)
+  
+  # simulate N independent rv uniformly distributed on the interval [0, T]
+  # these variables correspond to the jump times
+  U = sort(runif(N, min = 0, max = T))
+  
+  # initialization of the vector that should contain values of the stochastic 
+  # process at the given set of time points
+  X = rep(0, length(t))
+  
+  # values of the process without adding NAs at the times of jumps
+  X_withoutNAs = rep(0, length(t))
+  
+  # simulate jump sizes: N independent rv Y_i from a specified law
+  Y = rnorm(N, mean = 0, sd = 1)
+  
+  # fill vector X, i.e., calculate trajectory of the process
+  for (i in (1:length(t)) ) {
+    
+    # the trajectory is given by
+    term1 = sum((U<t[i])*Y)
+    X[i] = b*t[i] + term1
+    
+  }
+  
+  compoundPoissonProcess = list(processValues = X, time = t, drift = b, 
+                                jumpIntensity = lamda)
+  
+  class(compoundPoissonProcess) <- "compoundPoisson"
+  compoundPoissonProcess
+}
+
+# object of the class compoundPoisson
+instance1 = compoundPoisson(0,20)
+
+#
+# plot method for the class compoundPoisson ------------------------------------
+#
+plot.compoundPoisson <- function(instance_compoundPoisson){
+  
+  # properties of the process to be plotted
+  process = instance_compoundPoisson$processValues
+  time = instance_compoundPoisson$time
+  dfPlot <- data.frame(time, process)
+  
+  # construct name of the file to save the plot (based on the given instance)
+  parameter1 <- instance_compoundPoisson$drift
+  parameter2 <- instance_compoundPoisson$jumpIntensity
+  name_of_plot <-paste0("process","CompoundPoisson","Drift",  as.character(parameter1),  
+                        "JumpIntensity", as.character(parameter2), ".pdf") 
+  
+  ggplot(dfPlot, aes(time, process)) + geom_point(size=1) + 
+    xlab("time") +
+    ylab("") +
+    ggtitle("compound Poisson process ") 
+    ggsave(name_of_plot, width = 6, height =4)
+}
+
+plot(instance1)
+
+#
+# density of the log returns in exponential Levy model -------------------------
+#
+
+# reserve the name of the function, and use UseMethod command to tell R to 
+# search for the correct function
+returnsDensity <- function(someClass) {
+  
+  UseMethod("returnsDensity", someClass)
+  
+}
+
+returnsDensity.compoundPoisson <- function(instance_compoundPoisson){
+  
+  # log returns of the process
+  log_returns = diff(instance_compoundPoisson$processValues, lag=1)
+  
+  
+  # construct name of the file to save the plot (based on the given instance)
+  parameter1 <- instance_compoundPoisson$drift
+  parameter2 <- instance_compoundPoisson$jumpIntensity
+  name_of_plot <-paste0("retDen","CompoundPoisson","Drift",  as.character(parameter1),  
+                        "JumpIntensity", as.character(parameter2), ".pdf") 
+  
+  # density of the log returns
+  pdf(name_of_plot, width = 6, height =4)
+  plot(density(log_returns,kernel="gaussian"), xlim=c(-0.05,0.05),
+       col = "blue3", main = "", xlab = "log returns",  ylab = "Density")
+  grid()
+  dev.off() 
+}
+
+# 
+returnsDensity(instance1)
+
+#
+# plot of the log returns ------------------------------------------------------
+#
+
+# reserve the name of the function, and use UseMethod command to tell R to 
+# search for the correct function
+returnsPlot <- function(someClass) {
+  
+  UseMethod("returnsPlot", someClass)
+  
+}
+
+returnsPlot.compoundPoisson <- function(instance_compoundPoisson){
+  
+  # log returns of the process
+  log_returns = diff(instance_compoundPoisson$processValues, lag=1)
+  
+  # construct name of the file to save the plot (based on the given instance)
+  parameter1 <- instance_compoundPoisson$drift
+  parameter2 <- instance_compoundPoisson$jumpIntensity
+  name_of_plot <-paste0("retPlot","CompoundPoisson","Drift",  as.character(parameter1),  
+                        "JumpIntensity", as.character(parameter2), ".pdf") 
+  
+  # density of the log returns
+  # plot of log returns
+  pdf(name_of_plot, width = 6, height =4) # plot_name: variable from global environment
+  plot(log_returns, type = "l", xlab = "",  ylab = "log returns", main = "")
+  grid()
+  dev.off() 
+}
+
+returnsPlot(instance1)
+
+
+