A framework for valuing derivative securities

This paper develops a general framework for valuing a wide range of derivative securities. Rather than focusing on the stochastic process of the underlying security and developing an instantaneously-riskless hedge portfolio, we focus on the terminal distribution of the underlying security. This enables the derivative security to be valued as the weighted sum of a number of component pieces. The component pieces are simply the different payoffs that the security generates in different states of the world, and they are weighted by the probability of the particular state of the world occurring. A full set of derivations is provided. To illustrate its use, the valuation framework is applied to plain-vanilla call and put options, as well as a range of derivatives including caps, floors, collars, supershares, and digital options.

An empirical framework for studying desistance as a process

Recent reviews of the desistance literature have advocated studying desistance as a process, yet current empirical methods continue to measure desistance as a discrete state. In this paper, we propose a framework for empirical research that recognizes desistance as a developmental process. This approach focuses on changes in the offending rare rather than on offending itself We describe a statistical model to implement this approach and provide an empirical example. We conclude with several suggestions for future research endeavors that arise from our conceptualization of desistance.