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on Forecasting |
| By: | Alina Beygelzimer; John Langford; David Pennock |
| Abstract: | In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the average participant. The market price---an average or at least aggregate of traders' beliefs---offers a better estimate than most any individual trader's opinion. In this paper, we ask a stronger question: how does the market price compare to the best trader's belief, not just the average trader. We measure the market's worst-case log regret, a notion common in machine learning theory. To arrive at a meaningful answer, we need to assume something about how traders behave. We suppose that every trader optimizes according to the Kelly criteria, a strategy that provably maximizes the compound growth of wealth over an (infinite) sequence of market interactions. We show several consequences. First, the market prediction is a wealth-weighted average of the individual participants' beliefs. Second, the market learns at the optimal rate, the market price reacts exactly as if updating according to Bayes' Law, and the market prediction has low worst-case log regret to the best individual participant. We simulate a sequence of markets where an underlying true probability exists, showing that the market converges to the true objective frequency as if updating a Beta distribution, as the theory predicts. If agents adopt a fractional Kelly criteria, a common practical variant, we show that agents behave like full-Kelly agents with beliefs weighted between their own and the market's, and that the market price converges to a time-discounted frequency. Our analysis provides a new justification for fractional Kelly betting, a strategy widely used in practice for ad-hoc reasons. Finally, we propose a method for an agent to learn her own optimal Kelly fraction. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6655&r=for |
| By: | Martin Gremm; Mark B. Wise |
| Abstract: | Social Security and other public policies can be viewed as a series of cash in and outflows that depend on parameters such as the age distribution of the population and the retirement age. Given forecasts of these parameters, policies can be designed to be financially stable, i.e., to terminate with a zero balance. If reality deviates from the forecasts, policies normally terminate with a surplus or a deficit. We derive constraints on the cash flows of robust policies that terminate with zero balance even in the presence of forecasting errors. Social Security and most similar policies are not robust. We show that non-trivial robust policies exist and provide a recipe for constructing robust extensions of non-robust policies. An example illustrates our results. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6340&r=for |
| By: | Jeroen V.K. Rombouts (HEC Montréal, CIRANO, CIRPEE and Université catholique de Louvain, CORE); Lars Stentoft (HEC Montréal, CIRANO, CIRPEÉ, and CREATES); Francesco Violante (Maastricht University and Université catholique de Louvain, CORE) |
| Abstract: | We assess the predictive accuracy of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set 248 multivariate models that differ in their specification of the conditional variance, conditional correlation, and innovation distribution. All models belong to the dynamic conditional correlation class which is particularly suited because it allows to consistently estimate the risk neutral dynamics with a manageable computational effort in relatively large scale problems. It turns out that the most important gain in pricing accuracy comes from increasing the sophistication in the marginal variance processes (i.e. nonlinearity, asymmetry and component structure). Enriching the model with more complex correlation models, and relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a smaller way. Apart from investigating directly the value of model sophistication in terms of dollar losses, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performance. |
| Keywords: | Option pricing, Economic Loss, Forecasting, Multivariate GARCH, Model Confidence Set |
| JEL: | C10 C32 C51 C52 C53 G10 |
| Date: | 2012–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-04&r=for |