Nowadays the knowledge about pricing of ordinary derivatives is generally used and investors become interested in more complex products such as the exotic options. For people dealing with options in the market it is important to be able to price these specific derivatives. In this book, we focus on the pricing and modeling of such derivative products. So far, the Black-Scholes model has a huge influence on the way that traders price and hedge options. Despite the successes of Black-Scholes model, it has some shortcomings, emerged from many empirical investigations. Many models are produced to modify Black-Scholes model. Our objective was to consider the Kou model, to use the Laplace transform and it's Euler inversion algorithm to price plain vanilla and exotic options. We applied the research results to valuation of options in the real market. We wrote our own program in the software for statistical computing R and presented results on the example of the NASDAQ OMX Stocholm Market, considering the two-asset correlation options. We can assert that the observable option pricing method can be implemented to the real market and it will be useful for the market participants.