Demonstrate how to estimate the price of a European call option using Monte Carlo (MC)
simulation in R programming.
You will consider pricing a hypothetical Amazon.com option with a strike price of $450
as of the end of 2013 and 2.5 years to maturity. On 12/30/2013, the Amazon.com stock
price was $532.79 and the annualized standard deviation of its daily returns was
approximately 32%. As of that date, the annualized risk-free rate was 1%.
Please include all your relevant coding in R programming, answer(s) for each section as
well as explain your answer(s) clearly according to the tasks below:
a) Construct the variables for stock, sigma, strike, maturity time period and risk-free
rate.
b) Determine how many paths you will want to stimulate and why did you chose that
much.
c) Setup the parameters for your model of stock price behavior.
d) Calculate the value of the call option for each sample path.
e) Calculate the value of the put option in the same manner with the only change is in
the way we calculate the intrinsic value at maturity.
f) Compare the call and put option values of Monte Carlo with the Black Scholes call
and put option values for the same option.