The Variance Gamma Process and Option Pricing

A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S & P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model developed here.     

When Stress Frustrates and When It Does Not: Configural Models of Frustrated versus Mellow Salespeople

The purpose of this study is to elucidate the stress–strain relationship by examining compound causes of frustration in the workplace. Drawing on configuration theory, this article describes stress patterns, that is, configurations of role stressors and social stressors, and underlying frustration and its negation, that is, mellowness. In addition, this article describes potential sources of such frustration‐stimulating stress patterns by examining constellations of employee and task characteristics. Based on a sample of 118 salespeople, the authors analyze the data using fuzzy‐set Qualitative Comparative Analysis—an analytic method pertinent to describing configurational patterns of causal factors. The findings from this study indicate the coexistence of alternative patterns of stressors for frustration. In addition, the findings show that configurational patterns for frustrated salespeople are quite different from those characterizing mellow salespeople. In summary, knowledge of these constellations of stressors helps sales managers detect conditions that frustrate, and develop strategies to diminish these conditions in order to improve sales force performance.     

Evaluation of variants of economic regulation with the help of interregional “payments-income” tools

A pioneering experience in upgrading interregional models of intersectoral balance to “payments-income” systems that involve the financial side of production ties is described. Optimizing models of this class have been combined with tools for calculating aggregative price indices, which allows one to make up summary intersectoral, regional, and interregional financial balances for different forecast variants of the physical (material) production pattern.     

Evolutionary dynamics on infinite strategy spaces

Summary. The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies. Received: June 25, 1999; revised version: January 31, 2000     

SIMPLE PROCESSES AND THE PRICING AND HEDGING OF CLIQUETS

For data on market prices for 246 cliquets we consider pricing these exotic options using a relatively simple path space. The path space is subsequently stressed to market implied stress levels as well as stress levels predicted from contract characteristics. An additive process transitioning from a Sato process to a Levy process is formulated and estimated on vanilla options. Ask prices constructed from predicted stress levels are observed to have an in sample correlation of 92% with market prices. Interestingly, it is observed that capped cash flows have negative stress levels while uncapped products have positive stress levels. We illustrate the effect of hedging cliquet liabilities using call options as hedging assets permitting a 10% reduction in ask prices.