A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.     

Analysis of Beef Producers' Risk Management Perceptions and Desire for Further Risk Management Education

Beef cattle producers were surveyed in Texas and Nebraska to investigate perceptions of sources of risk, the effectiveness of risk management strategies, and interest in further risk management education, particularly production risk, using probit analysis. Important decision variables identified are age, prior use of risk management tools, previous attendances of risk management education, and risk aversion. Severe drought and cattle price variability are identified as primary risk factors with potential to affect farm income. Extremely cold weather and disease are of less importance. Understocking pasture and storing hay are perceived most effective as risk management options.     

Monopoly, competition and information acquisition

An incumbent monopolist is uncertain about its linear demand, but can acquire public information at a cost. We determine how an entry threat affects the firm's information acquisition. If returns to scale are constant and the state-contingent demands become more dispersed as output increases, then entry reduces information acquisition. If, however, either the incumbent or entrant has increasing returns; or if the state-contingent demands are nonlinear or fail increasing dispersion, then entry can increase information. Finally, entry can hurt consumers. Although entry always increases output, it can decrease information. Consumers sometimes prefer a better informed monopoly to a duopoly.     

Estimating the effectiveness of extension information systems using farm trials and subjective probabilities

A method of combining survey data and Dairy Herd Improvement Association (DHIA) records to achieve low cost farm trials is presented. Farm trials and surveys of current practices and production responses are useful to identify yield gaps between expectations predicted from experimental findings and actual field results. Different management schemes can be ranked using subjective probabilities and stochastic dominance to enhance successful implementation of research findings and to increase the feedback between researchers, extension workers, and producers. A survey of current masitis control practices and expected milk yield response is the example. Combining survey results with DHIA records allowed estimating the relationship between somatic cell counts (SCC) and milk yield. Eliciting beliefs about the relationship between SCC and milk yield showed that producers agreed with predictions from the statistical model. Subjective probabilities about SCC and mastitis control practices showed that our sample of experts and producers consistently ranked the different practices but extension agents had no consensus about the the most or least effective ones.     

A comparison of several approximations to the power function of the likelihood ratio test in covariance structure analysis*

In this paper we compare alternative asymptotic approximations to the power of the likelihood ratio test used in covariance structure analysis for testing the fit of a model. Alternative expressions for the noncentrality parameter (ncp) lead to different approximations to the power function. It appears that for alternative covariance matrices close to the null hypothesis, the alternative ncp's lead to similar values, while for alternative covariance matrices far from H_o the different expressions for the ncp can conflict substantively. Monte Carlo evidence shows that the ncp proposed in Satorra and Saris (1985) gives the most accurate power approximations.