Programming) Consider a European call option over an underlying asset whose price at time 0 is 105 dollars, with strike price K = 110 dollars, exercise time 1 year, interest rate equal to 5% (i.e. rT = 0.05), and a volatility such that σ √ T = 0.3
1. Compute the price of the call using the Monte Carlo method applied to the formula
with 1000 simulations. Find (approximately) the variance of the random variable whose expectation you are trying to evaluate, and give a confidence interval for the desired quantity
2. Do the same computation (including the confidence interval) combining the same method applied to the formula for the price of the put,
with the same number of simulations, and the call-put parity formula.