Commonly, equilibrium security prices are modeled by continuous‐state stochastic processes, while observed prices are rounded into discrete units. This paper models the rounding mechanism and examines the probabilistic structure of the resultant rounded process. We provide accurate and simple estimates of the inflation in estimated variance and kurtosis induced by ignoring rounding. In particular, the maximum‐likelihood estimate of security price volatility using rounded prices is developed, and a simulation analysis is performed to examine the small‐sample properties of this estimator. For many practical applications, a simple correction for rounding becomes available.

Commonly, equilibrium security prices are modeled by continuous-state stochastic processes, while observed prices are rounded into discrete units. This paper models the rounding mechanism and examines the probabilistic structure of the resultant rounded process. We provide accurate and simple estimates of the inflation in estimated variance and kurtosis induced by ignoring rounding. In particular, the maximum-likelihood estimate of security price volatility using rounded prices is developed, and a simulation analysis is performed to examine the small-sample properties of this estimator. For many practical applications, a simple correction for rounding becomes available.

The specification of a statistical distribution which accurately models the behavior of stock returns continues to be a salient issue in financial economics. With the introduction of arithmetic and geometric Brownian motion models, much attention has recently focused on a Poisson mixture of distributions as an appropriate specification of stock returns. For example, see [12], [3], [8], [10], [5], and [1]. Consistent with empirical evidence, these models yield leptokurtic security return distributions and, furthermore, the specification has much economic intuition. In particular, one may always decompose the total change in stock price into “normal” and “abnormal” components. The “normal” change may be due to variation in capitalization rates, a temporary imbalance between supply and demand, or the receipt of any other information which causes marginal price changes. This component is modelled as a lognormal diffusion process. The “abnormal” change is due to the receipt of any information which causes a more than marginal change in the price of the stock and is usually modeled as a Poisson process.

This paper provides a closed-form, preference-free means of valuing a European call option written on a default-free pure discount bond. Investors may not agree upon a theory of the term structure, but they will necessarily agree on equilibrium option values. Further, these equilibrium option values may be obtained without recourse to numerical approximation.Default-free pure discount bond prices were posited to follow a non-standardized transformed Brownian bridge process. This specification implicitly incorporates the terminal constraint that the price of a default-free pure discount bond equal its face value at maturity.Contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities. The Brownian bridge specification permits an appropriate means of incorporating a number of such constraints. Therefore, while this paper has considered only the application of the Brownian bridge process to the valuation of debt options, the introduction of this process may provide for many further financial applications.

Clifford A. Ball, Adrian E. Tschoegl, The Decision to Establish a Foreign Bank Branch or Subsidiary: An Application of Binary Classification Procedures, The Journal of Financial and Quantitative Analysis, Vol. 17, No. 3 (Sep., 1982), pp. 411-424

This paper introduces an event-study method that incorporates the possibility of a random event date. Consistent with empirical evidence, we assume an event may affect not only the conditional mean of a security's return, but also its conditional variance. We compare the statistical power and efficiency of our maximum-likelihood method with the standard application of traditional event-study methods to multiday security returns. Assuming a two-day event period, our empirical results provide evidence that the multiday approach is robust. We use our maximum-likelihood method to investigate the valuation effects of stock splits and stock dividends.

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 mean‐reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news.

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 mean‐reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news.

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at‐the‐money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.