The thesis consists of two parts. The first two essays deal with issues of infrequent trading of stocks, and the third essay concerns a contract called a right of first refusal (RFR). Based on the Beveridge and Nelson (1981, Journal of Monetary Economics) decomposition of an ARIMA process, the first essay develops a measure of true stock index value which is unobservable due to infrequent trading of stocks. This new and simple measure might well prove useful in studies of, say, lead-lag relationships between cash index and index derivatives markets, and the futures basis measurement. The second essay derives a discrete-time equilibrium pricing formula for European index options where index returns follow an ARMA process due to infrequent trading of stocks. In comparison with standard theoretical option prices the model indicates that the market for the Russell 2000$\sp\circler$ index options rationally adjusts for the effect of infrequent trading on volatility forecasts, but does not seem to correct options' underlying index value for the predictability induced by infrequent trading. The third essay builds a model of a partnership where the partners may decide to have a RFR for risk-sharing purposes. However, an empirical hypothesis derived from the model is not supported by data from Finnish private manufacturing partnerships. Reasons for the empirical failure of the model as well as alternative explanations for the popularity of RFRs are proposed. The model's results can also be taken normatively to help with decisions concerning RFRs in practise.