Similar to Airbnb, this will not affect the current booking's price. However, in the event that the reservation is canceled, the newly available dates will be priced at your most recently updated rate.
For example, let's assume that John Doe has booked one of your listings for 4 nights during October, at a rate of $100/night. If you then change October's pricing to $120/night, John Doe will still pay $100 a night for his existing reservation. However, if John Doe cancels his booking, those 4 nights that are now free will be listed at $120/night.