In an arbitrage‐free economy, there will always exist a set of linear operators which map future contingent dividends of securities into their current prices. It happens that such operators will also form an “evolution semigroup” as a consequence of intertemporal analysis of the no‐arbitrage restriction. This paper summarizes some of the major implications of the semigroup properties, but avoids almost all of the technical discussion which underlies them. Instead, several practical examples are presented. Some well‐known continuous‐time results are replicated by this alternative method, and certain new developments are explored.

In an arbitrage-free economy, there will always exist a set of linear operators which map future contingent dividends of securities into their current prices. It happens that such operators will also form an “evolution semigroup” as a consequence of intertemporal analysis of the no-arbitrage restriction. This paper summarizes some of the major implications of the semigroup properties, but avoids almost all of the technical discussion which underlies them. Instead, several practical examples are presented. Some well-known continuous-time results are replicated by this alternative method, and certain new developments are explored.

The due‐on‐sale clause contained in most conventional home mortgage contracts is equivalent to a prepayment penalty equal to the difference between the face value and market value of the loan. We analyze a bilateral game with asymmetric information and show that the bank demands the full penalty unless the market value of the loan is sufficiently low. In that case, the bank demands a prepayment penalty which is independent of the market value of the loan in order to induce additional prepayments. We also demonstrate, by a risk‐sharing argument, that the due‐on‐sale clause is optimal in some settings, even though it eliminates some beneficial home sales.

This study examines whether the information implied by simultaneous levels of option and stock prices (specifically, the implied standard deviation of returns) reflects other contemporaneously available information. The independent contemporaneous measure considered is the observed dispersion (across several financial analysts), at a point in time, in the forecasts of earnings per share for a given firm. The results indicate that implied standard deviations clearly reflect the contemporaneous dispersion in analysts' forecasts incrementally , i.e., beyond the information contained in the historical time series of returns.