Geometric Asian option: Geometric Ornstein-Uhlenbeck process

Master Thesis


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University of Cape Town

Asian options, also known as average value options, are exotic options whose payoffs are dependent on the average prices of the underlying assets over the life of the options. The Asian options are very popular among the market participants when dealing with thinly traded commodities because the average property of the Asian options makes it very difficult to manipulate the payoffs of the options. Another reason for the popularity of Asian options is that they are cheaper than the corresponding portfolio of standard options to hedge the same exposure. The pricing of Asian options has been the subject of continuous studies. In previous studies, Asian options have been priced based on the assumption that the underlying asset follows a geometric Brownian motion. This dissertation, however, assumes that the underlying asset follows a geometric Ornstein-Uhlenbeck process and provides an explicit formula for the geometric Asian options. The geometric Ornstein-Uhlenbeck process is more economically appropriate than the geometric Brownian motion for modelling commodity prices, exchange rates and interest rates due to its mean-reverting property.