The Black-Scholes call option pricing model exhibits systematic empirical biases. The Merton call option pricing model, which explicitly admits jumps in the underlying security return process, may potentially eliminate these biases. We provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of NYSE listed common stocks. However, we find no operationally significant differences between the Black-Scholes and Merton model prices of the call options written on the sampled common stocks. EMPIRICAL EVIDENCE CONFIRMS THE systematic mispricing of theBlack-Scholes call option pricing model. These biases have been documented with respect to the call option's exercise price, its time to expiration, and the underlying common stock's volatility. Black [3] reports that the model overprices deep in-the-money options, while it underprices deep out-of-the-money options. By contrast, MacBeth and Merville [10] state that deep in-the-money options have model prices that are lower than market prices, whereas deep out-of-the-money options have model prices that are higher. These conflicting results may perhaps be reconciled by the fact that the studies examined market prices at different points in time and these systematic biases vary with time (Rubinstein [16 ]). Employing over-the-counter data, Black and Scholes [4] also document that the model underprices both calls written on low volatility stocks and calls near to expiration, while the model overprices calls written on high volatility stocks.A number of explanations for the systematic price bias have been suggested (Geske and Roll [6]). Among these is the fact that the Black-Scholes assumption of a lognormally distributed security price fails to systematically capture important characteristics of the actual security price process. Merton [11, 12] has put forward an option pricing model that explicitly admits jumps in the underlying security return process, and which may resolve these pricing discrepancies. According to the Merton specification, the arrival of normal information leads to price changes which can be modelled as a lognormal diffusion, while the arrival of abnormal information, which can be modelled as a Poisson process, gives rise * Both authors from the Graduate School of Business Administration, The University of Michigan. We thank Phelim Boyle, Robert Jarrow, Eric Kirzner, William Margarabe, Robert Merton, and Stuart Turnbull for helpful suggestions. Michael Jenkins, David Sauer, and Michael Weisbach provided excellent research assistance. The comments of an anonymous referee are gratefully acknowledged. This work was supported by summer research grants from the Graduate School of Business Administration at The University of Michigan. Any remaining errors are the authors' responsibility. 155 156 The Journal of Finance to lognormally distributed jumps in the security return. If the underlying security return follows the Poisson jump-diffusion process, then the resultant equilibrium c...

his article uses data from the London gold market to investigate the nature, T frequency, and causes of rounding in transactions prices. The degree of price resolution-whether prices are quoted to the nearest 5, 10, 25, 50, or 100 centsis not constant, but rather is a function of the amount of information in the market, and the level and variability of the price. This article, therefore, provides further insight into the determination of prices in competitive markets.The fact that transactions actually occur at eighths (stocks) or twentieths (gold), rather than at some nth place decimal, is important from the point of view of the microeconomics of price formation. Economic theory has made much of the optimality of equilibrium prices. However, as Goldman and Beja (1979) point out, economic theory is less informative with regard to the effect of institutional arrangements on the actual functioning of markets. This article addresses one such aspect of a market's microstructure. The implications of the results are that (1) all returns are measured with error and that therefore all empirical work is subject toWe would like to thank

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This paper estimates a stochastic volatility model of short-term riskless interest rate dynamics. Estimated interest rate dynamics are broadly similar across a number of countries and reliable evidence of stochastic volatility is found throughout. In contrast to stock returns, interest rate volatility exhibits faster meanreverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility ref lects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news.THE PAST DECADE HAS WITNESSED UNPRECEDENTED GROWTH in the market for fixedincome derivatives, domestically as well as internationally. In light of this growth, recent research has attempted to empirically characterize the dynamics of short-term riskless interest rates necessary for the valuation of many of these securities. With few exceptions much of this evidence has been concerned with the behavior of U.S. interest rates. The purpose of this paper is to investigate the dynamics of short-term interest rates across a number of countries.A particularly noteworthy feature, at least of the U.S. evidence, is that the volatility of short-term interest rates is itself volatile. The stochastic nature of volatility is an important property of interest rate dynamics which we wish to focus on in our comparison. To do so practically, this paper implements a computationally efficient and statistically reliable method for estimating stochastic volatility models in finance. We apply this method to Chan et al.'s~1992! specification of short-term riskless interest rate dynamics augmented with stochastic volatility.For a clean international comparison, we use proxies for short-term riskless interest rates drawn from the same market, the London interbank market, over the same sample period.