Financial markets comprise the trading of stocks, bonds, currencies, and commodities. They also comprise the markets for products derived from the aforementioned securities such as the different varieties of futures, forwards, options, and swaps.; During the last two decades, the growth in the number and volume of daily transactions concluded on these markets has been overwhelming. This spectacular expansion was paralleled by a substantial qualitative improvement in deriving pricing techniques for the financial securities and their derivatives.; Sophisticated results are known under the assumption of a complete market setting. However, the pricing of derivatives securities under an incomplete market appears to be one of the most difficult problems in mathematical finance. For instance, very few results are known in the case of exotic options in general and barrier options in particular.; The aim of this work is to generalize the pricing formulas for plain vanilla options in the incomplete market setting. We then develop a pricing methodology for exotic options under the same setting. A comparative study is also presented to determine what kind of model (Gaussian or non-Gaussian) should be used to price plain-vanilla or exotic options.
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