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Many alternative models have been developed lately to generalize the BlackScholes option pricing model in order to incorporate more empirical features. Brownian motion and normal distribution have been used in this BlackScholes optionpricing framework to model the return of assets. However, two main points emerge from empirical investigations: (i) the leptokurtic feature that describes the return distribution of assets as having a higher peak and two asymmetric heavier tails than those of the normal distribution, and (ii) an empirical phenomenon called "volatility smile" in option markets. Among the recent models that addressed the aforementioned issues is that of Kou (2002), which allows the price of the underlying asset to move according to both Brownian increments and doubleexponential jumps. The aim of this thesis is to develop an analytic pricing expression for American options in this model that enables us to eciently determine both the price and related hedging parameters.
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