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Static hedging of geometric average Asian options with standard options. (English) Zbl 1320.91160
Summary: In this article, we first establish a theorem that represents the price of an Asian option in terms of standard European options with a shorter term and different strikes. Then using Gauss-Hermite numerical integration, we discretize our theorem so as to use Monte Carlo simulation to examine the error of the static hedging under the Black-Scholes model and the Merton jump-diffusion model. For ease of comparison, we also provide the error of the dynamic hedging. The numerical results show that the static hedging strategy performs better than the dynamic one under both models.
##### MSC:
 91G60 Numerical methods (including Monte Carlo methods) 62P05 Applications of statistics to actuarial sciences and financial mathematics 91G20 Derivative securities (option pricing, hedging, etc.)
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