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


-> 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)

  • $\begingroup$ What is the difference between "price at maturity" and "payoff"? I.e. between approach A and B? $\endgroup$
    – g g
    Commented Dec 20, 2015 at 17:34
  • $\begingroup$ 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 $\endgroup$
    – Michal
    Commented Dec 20, 2015 at 19:36

1 Answer 1


The right way is approach A. Approach B does not work because of the Jensen inequality. Take note that your confidence intervals are only asymptotically correct. Depending on the number of scenarios, your options and their parameters these might provide bad coverage.


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