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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? $\endgroup$ – SRKX Sep 29 '15 at 8:18
  • $\begingroup$ yes -- every pay-off is replicable. $\endgroup$ – Mark Joshi Sep 29 '15 at 22:44

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