The memory of a phoenix (phoenix product) that allows the holder, as an option, to change the manner in which the payoff (coupon) is determined so that it includes payment of the current coupon and any previous coupons that were not paid earlier because on those coupon dates the underlying did not hit/ breach the coupon barrier. This holds on any coupon observation date that the underlying hits/ breaches the coupon barrier. For a phoenix, coupon may be autocalled if the underlying price hits the lower barrier in the structure (where accumulated coupon will be forgone- a feature that sets a phoenix memory apart from a snowball).

Under memory setting:

Payment = current coupon + any previous non-paid coupon

If the coupon barrier level is below the autocall barrier level, the holder can have memory as an option.