Additive and Multiplicative Uncertainty Revisited: What Explains the Contrasting Biases?

above the certainty level while for additive uncertainty the price should be lower than the certainty level. This note gives an intuitive explanation for the result after first presenting a parsimonious review of the two models. We also discuss which, if either, of the two models is more realistic. Received December 14, 2001; revised version received July 16, 2002 Published online: April 30, 2003 We thank referees for helpful comments. Ciaran Driver would like to acknowledge the research facilities from ANU, Canberra for their help in writing this paper.     

Market Liquidity and Trading Activity

Previous studies of liquidity span short time periods and focus on the individual security. In contrast, we study aggregate market spreads, depths, and trading activity for U.S. equities over an extended time sample. Daily changes in market averages of liquidity and trading activity are highly volatile and negatively serially dependent. Liquidity plummets significantly in down markets. Recent market volatility induces a decrease in trading activity and spreads. There are strong day-of-the-week effects; Fridays accompany a significant decrease in trading activity and liquidity, while Tuesdays display the opposite pattern. Long- and short-term interest rates influence liquidity. Depth and trading activity increase just prior to major macroeconomic announcements.     

Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.