I like that idea @Samar1! Could also be good the other way around! If you want to fill it up closer to the date and you offer a discount on your regular price, would be nice if this was visible in the search results. Even though you can have a price range in the search criteria, you would probably be more likely to book something on discounted price... Everyone likes a bargain, or at least the idea of getting a bargain (even if it's not;-))
But have to admit I don't think it's possble with the calendar features in place at this moment 😞 You can amend your pricing per day/week/month, although it seems like a lot of work to start with opening days with a lower price and changing it when times goes by and then maybe changing it again to a lower price when the dates come closer. Smart pricing for you an option maybe?!
Good luck with hosting!