Options and efficiency in multidate security markets

This paper extends the work of Ross (1976; Q. J. Econ. (90) 1, 75-89) to multidate security markets. First, we show that if a primitive security separates states at the terminal date, then there exist multiperiod European options on that security generating dynamically complete markets. Second, we show that if a primitive security conditionally separates states at the terminal date, then there exist multiperiod European options on that security generating generically dynamically complete markets provided that certain conditions hold. Third, we show that there are economies for which the minimum number of multiperiod European options on a primitive security generating generically dynamically complete markets is relatively large. Finally, we show that in these economies, a relatively small number of multiperiod European options on possibly different portfolio strategies of primitive securities generates generically dynamically complete markets.