Abstract:

The presented paper deals with the methods of evaluating financial derivatives employing differential equations while focus is placed mostly on options contracts. The popular Black and Scholes model is derived, as well as its two less known modifications, namely that of Merton and Garman-Kohlhagen; moreover, the current status of scientific models following from the original Black-Scholes model is mapped. The paper refers to the considerable drawbacks and limitations of the option valuation models, in particular in turbulent times when economy diverges from standard conditions. Despite the countless number of modifications of the original Black-Scholes model that are often very complicated and unsolvable without the use of computer technology, traders keep using the original models for evaluating options contracts.