olliefr

# Generate a binomial lattice for American option.
genlattice.american <- function(Asset, Volatility, IntRate, DividendRate, Strike, Expiry, NoSteps, Payoff) {
  
  # The number of tree nodes to process.
  count <- sum(1 : (NoSteps+1))
  
  # This data frame will store asset and option prices.
  # The mapping from tree node (i,j) to linear index
  # inside the data frame will have to be computed.
  # The early exercise flag is also stored.

olliefr

# Generates a graph specification that can be fed into graphviz.
# Input: the binomial lattice produced by one of genlattice family functions.
dotlattice <- function(S, digits=2) {
  
  shape <- "plaintext"
  
  cat("digraph G {", "\n", sep="")
  cat("node[shape=",shape,"];","\n", sep="")
  cat("rankdir=LR;","\n")
  

olliefr

genlattice.vanilla.european.call <- function(Asset, Volatility, IntRate, DividendRate, Strike, Expiry, NoSteps) {
  return (genlattice.european(Asset=Asset, Volatility=Volatility, IntRate=IntRate, DividendRate=DividendRate, Strike=Strike, Expiry=Expiry, NoSteps=NoSteps, Payoff=payoff.vanilla.call))
}

genlattice.vanilla.european.put <- function(Asset, Volatility, IntRate, DividendRate, Strike, Expiry, NoSteps) {
  return (genlattice.european(Asset=Asset, Volatility=Volatility, IntRate=IntRate, DividendRate=DividendRate, Strike=Strike, Expiry=Expiry, NoSteps=NoSteps, Payoff=payoff.vanilla.put))
}

olliefr

# Generate a binomial lattice for European option.
genlattice.european <- function(Asset, Volatility, IntRate, DividendRate, Strike, Expiry, NoSteps, Payoff, Type) {
  
  # The number of tree nodes to process.
  count <- sum(1 : (NoSteps+1))
  
  # This data frame will store asset and option prices.
  # The mapping from tree node (i,j) to linear index
  # inside the data frame will have to be computed.
  X <- data.frame(matrix(NA, nrow=count, ncol=2))

olliefr

payoff.vanilla.call <- function(Asset, Strike) {
  return( max(0, Asset - Strike) )
}

payoff.vanilla.put <- function(Asset, Strike) {
  return( max(0, Strike - Asset) )
}

olliefr

# generate a graph specification that can be fed into graphviz
# This function was borrowed Rory Winston: 
# http://www.theresearchkitchen.com/archives/738
dotlattice <- function(S, labels=FALSE) {
  shape <- ifelse(labels == TRUE, "plaintext", "point")

  cat("digraph G {", "\n", sep="")
  cat("node[shape=",shape,", samehead, sametail];","\n", sep="")
  cat("rankdir=LR;","\n")

olliefr

# Generate a binomial lattice
# for a given up, down, start value and number of steps
# This function was borrowed Rory Winston: 
# http://www.theresearchkitchen.com/archives/738
genlattice <- function(X0=100, u=1.1, d=.75, N=5) {
  X <- c()
  X[1] <- X0
  count <- 2

  for (i in 1:N) {

olliefr

// c++ -std=c++11 -Wall binomial-sum.cc -o binomial-sum

#include <cstdlib>
#include <iostream>
#include <numeric>
#include <random>
#include <vector>

using namespace std;

olliefr

m <- 400 * 0.5   #mean
v <- 400 * 0.25  #variance
s <- sqrt(v)     #stdev
p <- 1 - pnorm(219, m, s)
print(round(p, digits=2))

olliefr

n <- 400 # number of tosses in a single trial
m <- 220 # threshold of interest
s <- 0   # the sum of binomial coefficients
for (k in m:n) {
  s = s + choose(n,k)
}
p = s / 2^n
print(round(p, digits=2))