dc.contributor.advisor Xu, Hong-Kun. dc.contributor.author Mkhize, Ngenisile Grace Zanele dc.date.accessioned 2010-08-20T09:59:36Z dc.date.available 2010-08-20T09:59:36Z dc.date.created 2007 dc.date.issued 2007 dc.identifier.uri http://hdl.handle.net/10413/429 dc.description Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2007. dc.description.abstract An Asian option is an example of exotic options. Its payoff depends on the average of the underlying asset prices. The average may be over the entire time period between initiation and expiration or may be over some period of time that begins later than the initiation of the option and ends with the options expiration. The average may be from continuous sampling or may be from discrete sampling. The primary reason to base an option payoff on an average asset price is to make it more difficult for anyone to significantly affect the payoff by manipulation of the underlying asset price. The price of Asian options is not known in closed form, in general, if the arithmetic average is taken into effect. In this dissertation, we shall investigate the pricing theory for Asian options. After a brief introduction to the Black-Scholes theory, we derive the partial differential equations for the value process of an Asian option to satisfy. We do this in several approaches, including the usual extension to Asian options of the Black-Scholes, and the sophisticated martingale approach. Both fixed and floating strike are considered. In the case of the geometric average, we derive a closed form solution for the Asian option. Moreover, we investigate the Asian option price theory under stochastic volatility which is a recent trend in the study of path-dependent option theory. dc.language.iso en en_US dc.subject Exotic options (Finance) en_US dc.subject Option value. en_US dc.subject Theses--Mathematics. en_US dc.title The pricing theory of Asian options. en_US dc.type Thesis
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