Stock markets linkages and analysis of the arbitrage between spot and futures markets. The first part is devoted to examination of long and short term dependencies between markets. As an example of long term relationship between stock markets, the influence of US market on the most important markets during twenty years period was subject of examination. In turn, to examine short term relationship the dependencies between Japanese and Hong Kong markets during Asian crisis 1997 were scrutinized. The examination of stock of linkages was carried out by application of Markov Switching models. This approach has an advantage to the previous methods because it does not assume a priori a form of relationship between financial markets. Moreover, the Markov Switching framework allows calculating the probability that one market is in crisis or calm regime conditional on different sets of information about other markets. According to the obtained results the contagion between financial markets was rejected, however, sufficient facts supporting the presence of feedback spillovers were found. The second part of thesis presents results of detailed analysis of arbitrage opportunity between spot and futures markets on Polish blue chips index WIG 20. The Polish stock market is one of the emerging futures markets in Europe, it is characterised by proprieties which were absent in case of previous studies of arbitrage. The analysis shows that the lack of efficiency in arbitrage sense is due to the fact that investors have limited access to short sale, there is uncertainty about the size of interest rates, and dividends are paid in an irregular way. Finally, the thesis provide detailed mathematical derivation of the price of future contract and the value of forward contract on zero coupon bond when the short term interest rate is modelled by Cox-Ingersoll-Ross model. In addition, the thesis contains some comments on the methods of deriving price of contigent claims.