Economics Insights @ CBS

We propose and test a new approach for modeling consumer heterogeneity in conjoint estimation based on convex optimization and statistical machine learning. We develop methods both for metric and choice data. Like hierarchical Bayes (HB), our methods shrink individual-level partworth estimates towards a population mean. However, while HB samples from a posterior distribution that is influenced by exogenous parameters (the parameters of the second-stage priors), we minimize a convex loss function that depends only on endogenous parameters.

In this paper, we propose a method of accounting for stock options that tracks the effect of the options on shareholder value. The accounting approach we outline can be applied not only to employee stock options but to all claims that are effectively convertible into common shares, including convertible preferred stock, warrants, and call and put options on the firm's own stock. Our proposal also aims to make accounting consistent with stock prices, since the market surely takes account of the (potential) valuation effects of these claims when setting stock prices.

We investigate and compare two dual formulations of the American option pricing problem based on two decompositions of supermartingales: the additive dual of Haugh and Kogan (Oper. Res. 52:258-270, 2004) and Rogers (Math. Finance 12:271-286, 2002) and the multiplicative dual of Jamshidian (Minimax optimality of Bermudan and American claims and their Monte-Carlo upper bound approximation. NIB Capital, The Hague, 2003).