Another way to price the Double-no-touch option

Static replication is always the most elegant way of pricing. The no-arbitrage argument will let us say that if, at some time in the future, two portfolios have the same value for sure, then their price should be equal any time before this. We will show how double-knock-out (DKO) options could be used to build a DNT. We will need to use a trick; the strike price could be the same as one of the barriers. For a DKO call, the strike price should be lower than the upper barrier because if the strike price is not lower than the upper barrier, the DKO call would be knocked out before it could become in-the-money, so in this case, the option would be worthless as nobody can ever exercise it in-the-money. However, we can choose the strike price to be equal to the lower barrier. For a put, the strike price should be higher than the lower barrier, so why not make it equal to the upper barrier. This way, the DKO call and DKO put option will have a very...