Barrier options and their static hedges: simple derivations and extensions

We use a reflection result to give simple proofs of (well-known) valuation formulas and static hedge portfolio constructions for zero-rebate single-barrier options in the Black-Scholes model. We then illustrate how to extend the ideas to other model types giving (at least) easy-to-program numerical methods and other option types such as options with rebates, and double-barrier and lookback options.