Valuing and hedging exotic options, whose payoff is discontinuous and uncertain, normally requires an extensive knowledge of advanced mathematics. The solutions generated are seldom intuitive and rarely provide simple hedge. This thesis shows how certain types of exotic options can be valued and hedged without advanced mathematics. The hedging strategies are intuitive and rather simple. This simplicity arises from using standard options in the replicating portfolio along with the underlying asset.
To hedge binary option, whose payoff is all or nothing, we must prescribe a certain probability, p < 1, called the hedging probability. This, in turn, yields a dynamic hedging scheme similar to standard options but which hedges the binary with probability p. In case of barrier option, our hedges are static; there is no need to rebalance the replicating portfolio dynamically over time, which saves the hedger both transaction costs and headaches. Instead of continuously monitoring the underlying and trading with every significant price change, the hedger can place contingent buy and sell orders with start/stop prices at the barriers. The fundamental result underpinning the creation of replicating portfolio is put-call symmetry. By using this simple formula, we can engineer simple portfolios to mimic the values of standard options along barriers.
