There is no doubt that the Colosseum is one of the best known buildings in the world. It is the largest amphitheatre ever built and it still impresses to all those who visit Rome. The construction of the Colosseum began under the emperor Vespasian in the year 72; it was completed in the year 80, when the emperor was Divus Titus. In order to commemorate the inauguration of the building several series of sestertius were minted during the years 80-82 with a realistic representation of the Colosseum. These sestertius have several particularities. First, the obverse of the coin does not include the portrait of the emperor, as was the case in most sestertius; instead, it depicts the Colosseum. Second, the design is so well detailed that it even shows the statues of the building and the citizens inside it. Third, the perspective from which the Colosseum is depicted is almost unique; maybe it was the only way to show the inside and the outside of the building in a single image.
There is more information about this coin here and here.
Not surprisingly this sestertius is one of the most demanded coins from the Roman Empire. Collectors will search for it even in low quality (e.g. this one was hammered for 8.000 euros and this one for 8.000 GBP). In better conditions, but still in a lower grade than the one that is now on auction, we can see that the hammer price is between $90.000 and $125.000 (e.g. this, this and this). Hence, we can consider that this coin can worth something more than $125.000. However, this kind of coins sometimes reach surprising prices on auctions: two important collectors may want it and the price can end up being very high. This must have happened with this coin, whose hammer price was 380.000 CHF.
Description from the seller
Roman Imperial Coinage, Divus Titus, Sestertius, Rome, c. 81-2, view of the Coliseum, on left Meta Sudans, on right, porticoed building, rev. divo avg t divi vesp f vespasian, Titus, holding branch, seated left on curule chair, arms around, s c below, 26.13g (Elkins, NC 2006, D8, dies A5/P7, item c, this coin; RIC 131; BMC –; CBN 543; C 399). Very fine and extremely rare, only 10 specimens known of the Divo type, 7 of which are in institutions; one of the most important Roman bronze coins available to commerce and a full grade finer than the only other example sold recently (NAC Auction 86, 8 October 2015, lot 182 [80,000 Sw Fr]) ;£60,000-80,000 — Provenance: Ars Classica Auction XIII, 27-9 June 1928, lot 1201; J. Campion Collection, Glendining Auction, 30 November-3 December 1937, lot 205; bt Spink February 1939. Perhaps no architectural representation on Roman coinage is more recognised than the Flavian Amphitheatre (Roman Coliseum). The structure was begun under Vespasian but not completed until the reign of Titus and the dedication ceremony took place in 80. Funds for the build came from the spoils of war with the Jews and the treasure removed from the Jewish temple. More than Rome’s first permanent amphitheatre, the Coliseum celebrated the ideology and policy of the Flavian regime