This bachelor thesis examines the binomial tree algorithm as a tool for the numerical calculation of option prices. Starting from the historical approach of Cox, Ross and Rubinstein, the one-step binomial model is derived from basic no arbitrage principles. This simple model is then extended to multi-period models and the continuous time Black-Scholes model is shown to be a limiting case for infinitesimal time steps. The usefulness of the binomial model for actual numerical calculations of option prices with the binomial tree algorithm is explored. The binomial tree algorithm can be easily adapted to different types of problems, but in its basic form has a somehow mediocre performance. Therefore the optimal drift model is introduced, which is an easy implementable optimisation strategy and achieves results comparable to other numerical methods. The last part of the thesis explores the numerical calculation of option prices for options with multiple underlyings by multi-dimensional binomial trees, and shows how these algorithms can be optimized by decoupling the stock price processes of the underlyings.      «

This bachelor thesis examines the binomial tree algorithm as a tool for the numerical calculation of option prices. Starting from the historical approach of Cox, Ross and Rubinstein, the one-step binomial model is derived from basic no arbitrage principles. This simple model is then extended to multi-period models and the continuous time Black-Scholes model is shown to be a limiting case for infinitesimal time steps. The usefulness of the binomial model for actual numerical calculations of opti...     »