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We all know from text books and practice that a knock out call is usually cheaper than a vanilla call option. Economically speaking, this comes from the fact that there is a probability bigger than zero of future spot price movements hitting the barrier. Consequently, the knock out option does not participate in every possible future spot price scenarios and that is why we do not have to pay the same premium as for a vanilla call.

If we now have a look at a Down-and-out Call with Barrier below strike, we see that the price matches a plain vanilla call option.

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So, why should I buy a down and out call? Consider we hit the barrier below strike, then the option expires worthless. Consider the same case with a plain vanilla call. The option does not expire worthless and even has the possibility to participate on future spot upward movements. So why do we have to pay the same amount of premium for a down and out call as for a plain vanilla call?

Thanks,

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If we now have a look at a Down-and-out Call with Barrier below strike, we see that the price matches a plain vanilla call option.

This statement is false. The DAO Call is worth less than the plain vanilla Call. For instance if the Barrier is equal to the strike then the DAO Call is worth zero.

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  • $\begingroup$ ok, barrier = strike then of course the down and out barrier is worthless. But perhaps I am getting the point. For a down-and out call we put the barrier quite close below the strike. Like an very cheap and aggressive bet that spot will only rise. (Turbo Bull) $\endgroup$
    – Fugazi
    Commented Feb 1, 2018 at 14:49
  • $\begingroup$ In your example for a 3M expiry EURJPY option with current spot at 136.18 the risk neutral probability of EURJPY hitting 120 within the next 3M and ending above the current spot in 3M is very low, so the DAO call is worth almost the same than the plain vanilla call. $\endgroup$
    – Antoine Conze
    Commented Feb 1, 2018 at 15:06
  • $\begingroup$ ok, so what we see above is an asset specific phenomenon which results from current market conditions. Nevertheless if the barrier is much closer to current spot level, the price remains the same. $\endgroup$
    – Fugazi
    Commented Feb 1, 2018 at 15:11
  • $\begingroup$ That would be a bug in your screen. Perhaps a refresh problem after changing the barrier value ? $\endgroup$
    – Antoine Conze
    Commented Feb 1, 2018 at 15:13

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