Barrier Put-Call Transformations

Abstract

In this article we show a simple but important relationship between the put-call transformation and the put-call symmetry as well as extend the relationship to also hold for single and double barrier options. These new barrier transformations give new insight in barrier option valuation. Using the transformation it is possible to value a barrier put option from a barrier call option formula and vice versa. Our results also extend the possibilities for static hedging and closed form valuation for many new exotic options. The new relationships also make us able to value a double barrier option in a simple and intuitive way, only using a few single barrier options.