# How to calculate confidence interval for option price?

I model option prices for European call using Monte Carlo method. What is the proper way to calculate the confidence interval?

A. -> Calculate the payoffs (there will be number of zeros as some prices go below strike)
-> calculate mean and st.dev. of the payoffs
-> apply the formula for the confidence interval: mean option payoff +/- z*(st.dev option payoff / sqrt(number of simulation) )
-> discount

or

B.
-> Calculate the mean and st.dev. of all the prices at maturity -> apply the formula for the confidence interval: mean underlying priceT +/- z*(st.dev underlying priceT / sqrt(number of simulation) )
-> calculate upper and lower band of the payoffs
-> discount

where payoff is max(underlying asset priceT - option strike price,0)

• What is the difference between "price at maturity" and "payoff"? I.e. between approach A and B?
– g g
Commented Dec 20, 2015 at 17:34
• under PriceT I meant the price of underlying asset at T, under payoff the payment from exercising the option max(St-K,0) where K is the strike price of the call Commented Dec 20, 2015 at 19:36