This paper obtains equilibrium interest rate option prices for discontinuous short-term interest rate processes. The prices are first obtained for a general distribution of jump sizes using a process with a number of fixed size jumps. The pricing formulas are then used to obtain option prices when the jump distribution is known to be one of the continuous distributions. The commonly used jump-diffusion, stochastic volatility jump-diffusion, and Gamma process option prices can be obtained as limiting cases. The methodology is also applied to obtain the prices of options on stocks. Finally, the paper shows how portfolios to hedge derivative securities can be built.

Samuelson called accepting a sequence of independent positive mean bets that are individually unacceptable a fallacy of large numbers, and subsequent researchers have extended Samuelson's condition on utility functions to assure that they would not allow this fallacy. By contrast, some behavioralists, arguing the merits of diversification, believe that it is simply wrong headed to refuse a long series of independent “good” bets out of a misguided faith in expected utility theory. Contrary to what one might infer from the literature, this paper shows that accepting sequences of good bets is both consistent with expected utility theory and quite usual.

It is now widely held that stock prices are too volatile to be optimal forecasts of future dividends discounted at a constant rate. Using the present value model with a constant discount rate, we show that when there is memory in the duration of dividend swings, the stock price can move in a more volatile fashion than could be warranted by future dividend movements. The memory in the duration of a dividend swing will lead economic agents to time the swing, thereby generating a spurious bias in the stock price. When memory is strong, this spurious bias becomes significant and induces excess volatility in the stock price as if rational bubbles exist. The Efficient Method of Moments (EMM) procedure is used to examine the long swings property in the dividend series. We cannot reject the hypothesis of a strong memory in the dividend swings, and show that excess volatility, even in large samples, can be generated through simulation.

This study provides evidence that differential interpretations are an important stimulus for speculative trading. We measure differential interpretations using data on analysts' revisions of forecasts of annual earnings after the announcement of quarterly earnings that are components of those annual earnings numbers. We find two conditions under which differential interpretations play a significant role in explaining trading. First, we present empirical evidence supporting Kandel and Pearson's (1995) argument that trading coincident with small price changes reflects investors' differential interpretations of information. This evidence is important because it is inconsistent with conventional models of trade that assume homogeneous interpretations. Second, we also find that differential interpretations explain a significant amount of the trading occurring in a sample where trading volume is higher than the (firm-specific) non-announcement period average. This result is consistent with informed traders acting on their differential interpretations when there is enough liquidity trading to help camouflage their own information-based trades. In sum, the study's results confirm Bachelier's (1900) intuition that differential interpretations are an important stimulus for trading.

Trade execution costs remain larger on NASDAQ compared to the NYSE in the wake of new SEC-mandated order-handling rules and reductions in tick sizes, but the differential across markets is smaller than in earlier years. Cross-sectional regression analysis indicates that the differences in average trade execution costs are not explained by variation in observable economic factors. Quotations on both markets continue to cluster disproportionately on round fractions, and more so on NASDAQ than the NYSE, but quotation rounding appears not to be responsible for the greater NASDAQ execution costs. Preferencing agreements are highlighted as a likely reason that NASDAQ trade execution costs remain larger.

We distinguish among the signaling, free cash flow, and wealth transfer hypotheses in explaining the stock price reaction to specially designated dividend (SDD) announcements. In a direct test of the signaling power of SDDs, we find both a larger stock price reaction and a significant upward revision of earnings forecasts for firms with Tobin's q less than one, but not for other firms. Our results support the conditional signaling hypothesis, which predicts greater effects of favorable information for low q firms. Taken together, our results for stock price effects and earnings forecast revisions do not support either the free cash flow or wealth transfer hypotheses.