Static Hedging of Barrier Options under General Asset Dynamics

Abstract

The Black-Scholes model and most other modern derivatives pricing models are based on the idea of replicating an option9s payoff by dynamically trading between the underlying asset and riskless borrowing or lending. But dynamic hedging has always worked a lot better in theory than in practice, where transactions costs, stochastic volatility, non-diffusion price jumps, and other deviations from the model9s assumptions have to be dealt with. Barrier options in particular present problems because dynamic hedging becomes very difficult when the underlying asset price is near the barrier. An alternative approach that has been explored to some degree in the literature is static hedging, in which the payoff on an option is replicated by a static portfolio of other options. Several different ways to do this have been proposed, though they may entail unrealistic requirements, such as the existence of plain vanilla options with a continuum of strike prices. In this article, Nalholm and Poulsen present an implementable general static hedging technique for barrier options. It uses only contracts that are traded in the market and works for jump-diffusion processes with stochastic volatility, thus nesting the existing methods. Simulation results show that the technique performs substantially better than previous models. TOPICS:Options, futures and forward contracts

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