Barrier Options and Their Static Hedges: Simple Derivations and Extensions

We use a re ection result to give simple proofs of (well-known) valuation formu-las and static hedge portfolios 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, double-barrier and lookback options