If you bought an Equity Call Option with a Down-and-In Barrier, are you Long Skew or Short Skew? Please provide explanation as well. Thanks.
If spot moves down towards Knock-In Barrier, I want high vol (to knock the barrier). Therefore, I'm long low strike (long skew).
Down-and-In Barrier Option = Long Skew
Down-and-Out Barrier Option = Short Skew
Up-and-In Barrier Option = Short Skew
Up-and-Out Barrier Option = Long Skew
vanilla = down and out + down and in Vanilla is not skew sensitive.
The down and out can be modelled as a vanilla plus the vanilla pay-off geometrically reflected in the barrier. Its price will go up if the strike vol goes up or the reflected strike vol goes down. So we want skew if that means the high strike implied vols going up and the low strikes ones going down.
Opposite for the down and in.