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Static hedging strategies for barrier options and their robustness to model risk

Kaya, Orçun
With the rapid increase in the usage of barrier options on the OTC markets, pricing and especially hedging of these exotic instruments became an important field of research. This paper aims to explain, apply and compare current methods used for pricing and hedging barrier options with a simulation approach. An overview of most popular methods for pricing and hedging is presented in the first part, followed by application of these pricing methods and comparing the performances of different dynamic and static hedging techniques in Black-Scholes environment by simulation in the second part. In the third part different models such as ARCH type and Stochastic Volatility are used with different jump terms to relax the assumptions of the Black-Scholes and examine the effects of these incomplete models on both pricing and performance of different hedging techniques. In the fourth part diffusion models such as Constant Variance Elasticity, Heston Stochastic Volatility and Merton Jump Diffusion are used to complete the picture.