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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 ...


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In an interview on Tastytrade, NYU's Phil Maymin talks a bit about this exact question: https://www.tastytrade.com/tt/shows/what-else-ya-got/episodes/dr-philip-maymin-skew-10-22-2014?locale=en-US A full example of this is also covered in Maymin's book, Financial Hacking.


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It also depends on at what levels of the spot the higher vol gets realized. In your example: if you buy an option on a 40 vol expiring in a month and over the next month stock the average vol of the stock is 60 and you dynamically hedge, are you guaranteed to make money? If not could you please give me a simple example perhaps where you'd wind up ...



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