I'm valuing a type of barrier option. The (call) option knocks-in if the stock price maintains a target price (say 125% of the initial stock price) for 20 consecutive trading days. The strike price equals the starting stock price. In addition to determining the value of this option, I also have to determine the expected time it knocks-in, so I wrote a Monte Carlo.I ran the Monte Carlo 10,000 times. The result was higher than a standard knock-in barrier option (no 20-consecutive day provision). This makes no sense to me. On one hand, upon achieving the 20-consecutive day hurdle, the stock price should be higher than the barrier resulting in a higher value than a standard barrier. However, I would this is more than offset by the frequency of achieving the barrier on a single-touch basis vs. 20-consecutive day touch basis. Are my instincts right? Or does the model actually sound right?

Which RNG are you using ?

I wrote my company's ESO valuation engine as well, a few years ago. Your intuition sounds correct to me, that this is a code bug. However beware, are you comparing against a closed-form solution for a barrier option? If so, you need to make sure every other aspect of the comparison is valid ... i.e. constant risk-free rate with continuous compounding, constant dividend yield, constant volatility. Many times in ESO valuations this is not the case.If indeed this is the case, then you need to see if you can rule out simulation error. If it is a long-dated (i.e. 10y option) then the difference in prices for these instruments is very small and could be dwarfed by monte carlo error. Compute standard error of your estimate and see, you may just need more paths and/or a better generator as discussed by DCFC (I would recommend MT). Finally one other check you can run is to actually price the vanilla knock-in on the same set of paths you are pricing your ESO and compare all three results. If something still looks funky then you have a bug.Hope it helps

10,000 sounds too low. I would say 100,000 is the min.