I'm simulating dynamic delta hedging for up-and-out call option. For plain vanilla call options, I heard that the option price is the expected value of the accumulated delta hedging cost. Does it also hold for exotic option, like up-and-out call options?
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Yes.
If you use the BS Model for computing deltas and the same model for evolving the stock price then you should replicate the pay-off of any contract.
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$\begingroup$ Is it always possible to delta-hedge an exotic option in BS? $\endgroup$– SRKXCommented Sep 29, 2015 at 8:18
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$\begingroup$ yes -- every pay-off is replicable. $\endgroup$ Commented Sep 29, 2015 at 22:44