-- 60 * 60 * 24 = 86400 // number of seconds in day
WITH range AS (SELECT *,
                      EXTRACT(EPOCH FROM min) min_e,
                      EXTRACT(EPOCH FROM max) max_e
               FROM
		               (SELECT min(date) AS min, max(date) AS max FROM prices) s)
SELECT
	CASE WHEN prev_d <> min_e AND date <> g
		     THEN ROUND((m * g + ((price + prev_p) - m * (date + prev_d)) / 2)::NUMERIC, 2)
	     ELSE price END                                           price,
	date <> g           interpolated,
	TIMESTAMP WITHOUT TIME ZONE 'epoch' + g * INTERVAL '1 second' date
FROM
	(SELECT *,
	        generate_series(prev_d + 86400, date, 86400) g
	 FROM
		 (SELECT *,
		         (price - prev_p) / (date - prev_d) m
		  FROM
			  (SELECT
				   id,
				   range.min_e,
				   range.max_e,
				   EXTRACT(EPOCH FROM
				           (lag(date, 1, range.min) OVER (PARTITION BY entity_id ORDER BY date)))::BIGINT prev_d,
				   EXTRACT(EPOCH FROM date)::BIGINT                                                       date,
				   (lag(price, 1, price) OVER (PARTITION BY entity_id ORDER BY date))                     prev_p,
				   price
			   FROM
				   prices,
				   range) a
		     where date <> prev_d) b) c;