With the finance developed in modern days, options are traded by banks or other financial institutions on many exchanges all over the world. An option that can be exercised at any time during its life, the American style option is one of the most popular used among them. In this paper we implement Monte Carlo Simulations in order to price American options. The American option valuation by Monte Carlo methods was considered a very challenging problem for many years. The works from Carrière (1996) and Longstaff and Schwartz (2001) present an easy access to the American option pricing respectively the optimal stopping problem. This master thesis implements Monte Carlo algorithms for pricing vanilla and exotic options with and without the early exercise property of American options. The examples include algorithms for European, Asian and Parisian (or delayed Barrier) options. The convergence and efficiency is analyzed and some possible speedups are discussed.     «

With the finance developed in modern days, options are traded by banks or other financial institutions on many exchanges all over the world. An option that can be exercised at any time during its life, the American style option is one of the most popular used among them. In this paper we implement Monte Carlo Simulations in order to price American options. The American option valuation by Monte Carlo methods was considered a very challenging problem for many years. The works from Carrière (1996)...     »