This paper generalizes the nonparametric approach to option pricing of Stutzer (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie-Read family of divergence measures. While the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black-Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed.

We propose a Generalization of Roy's (1952) Safety First (SF) principle and relate it to the IID versions of Stutzer's (Stutzer's 2000, 2003) Portfolio Performance Index and underperformance probability Decay-Rate Maximization criteria. Like the original SF, the Generalized Safety First (GSF) rule seeks to minimize an upper bound on the probability of ruin (or shortfall, more generally) in a single drawing from a return distribution. We show that this upper bound coincides with what Stutzer showed will maximize the rate at which the probability of shortfall in the long-run average return shrinks to zero in repeated drawings from the return distribution. Our setup is simple enough that we can illustrate via direct calculation a deep result from Large Deviations theory: in the IID case the GSF probability bound and the decay rate correspond to the Kullback-Leibler (KL) divergence between the one-shot portfolio distribution and the “closest” mean-shortfall distribution. This enables us to produce examples in which minimizing the upper bound on the underperformance probability does not lead to the same decision as minimizing the underperformance probability itself, and thus that the decay-rate maximizing strategy may require the investor to take positions that do not minimize the probability of shortfall in each successive period. It also makes clear that the relationship between the marginal distribution of the one-period portfolio return and the mean-shortfall distribution is the same as that between the source density and the target density in importance sampling. Thus Geweke's (1989) measure of Relative Numerical Efficiency can be used as a measure of the quality of the divergence measure. Our interpretation of the decay rate maximizing criterion in terms of a one-shot problem enables us to use the tools of importance sampling to develop a “performance index” (standard error) for the Portfolio Performance Index (PPI). It turns out that in a simple stock portfolio example, portfolios within one (divergence) standard error of one another can have very different weights on individual securities.Entropy, Importance sampling, Kullback-Leibler divergence, Portfolio choice, Portfolio performance, Safety first, Shortfall,

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Using individual-level data from the 2008 National Study of the Changing Workforce, we quantify how workers' job satisfaction levels correlate with five schedule-based workplace flexibilities. The data permit us to control for numerous variables that might otherwise explain variation in the probability of job satisfaction, including, but not limited to, income, benefits, stress, depression, job control and individual preferences over flexibilities. Conditional on this control set, we find that workplace flexibilities correlate with an 8.1 per cent increase in job satisfaction. The relationship between job satisfaction and workplace flexibilities prevails through several sensitivity analyses, bias assessments and a propensity score matching analysis. We also explore how job satisfaction, union membership and workplace flexibilities intermix; we find that workplace flexibilities may function as a partial substitute for union membership.

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