Hedging of barrier options - Justino, Diogo Monteiro da Costa Soares (2010)
Barrier options are exotic options that can be difficult to hedge due to the possibility of the delta and gamma values being very large close to the barrier. This thesis investigates methods to hedge barrier options that can minimize the profits and losses that arise when using a dynamic technique known as delta hedging. We present two methods by Carr (1994) and Derman (1994) that create a static portfolio of vanilla options. The first method uses the put-call symmetry relationship and builds a portfolio of different options with the same maturity and different strikes. The second method divides time into intervals and tries to match the barrier option payoff at each of theses intervals with other vanilla options. The techniques are evaluated in the geometric Brownian motion environment where they were deduced and in real market conditions with time series of the S&P 500 index.