#  R code to calculate implied vol of a European put.
#  For the class Mathematics in Finance

#  http://www.math.nyu.edu/faculty/goodman/teaching/MathFin/index.html
# Author: Jonathan Goodman

rm(list=ls())

#     Parameters of the option

T_e  = .5    #   Expiration time, in years
K    = 2000  #   option strike price
r    = .01   #   risk free rate
S0   = 2     #   spot price

P_m = 8      #   market price of the put

sig_a = .05  #  lower bound for implied vol
sig_b = 10   #  upper bound for implied vol

#    Find the value of sigma so that P(sig) = P_m

source("OptionPricer.R")          #  Where the function that evaluates P(sig) is defined
source("BisectionSearch.R")       #  Where the nonlinear equation solver is defined

eps   = 10^(-5)
sig_i = solver( PutPrice, P_m, sig_a, sig_b, eps)

cat("The implied vol is ", sig_i, "\n")

objectList = ls()
for (objectName in objectList) {
    object = get0( objectName)
    cat("Object ", objectName, " has type ", typeof(object), "\n")
  }