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Price dynamics in political prediction markets

Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved November 25, 2008 (received for review May 23, 2008)
Abstract
Prediction markets, in which contract prices are used to forecast future events, are increasingly applied to various domains ranging from political contests to scientific breakthroughs. However, the dynamics of such markets are not well understood. Here, we study the return dynamics of the oldest, most datarich prediction markets, the Iowa Electronic Presidential Election “winnertakesall” markets. As with other financial markets, we find uncorrelated returns, powerlaw decaying volatility correlations, and, usually, powerlaw decaying distributions of returns. However, unlike other financial markets, we find conditional diverging volatilities as the contract settlement date approaches. We propose a dynamic binary option model that captures all features of the empirical data and can potentially provide a tool with which one may extract true information events from a price time series.
Footnotes
 ^{1}To whom correspondence should be addressed. Email: amaral{at}northwestern.edu

Author contributions: S.R.M., D.D., T.A.R., and L.A.N.A. designed research; S.R.M. and T.A.R. performed research; S.R.M., T.A.R., and L.A.N.A. analyzed data; and S.R.M., D.D., T.A.R., and L.A.N.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

↵ Binary options differ from ordinary options in three respects: (i) the payoff structure, (ii) the fact that there is no underlying traded asset, and (iii) pricing discontinuities at settlement, as we will show below.

↵ Small amounts of noise may arise from the bid–ask spread, asynchronous trading, and “stale” prices, though such factors should be small in active markets.

↵ See SI Appendix for details of the method and the results. To make sure that those results are not due to the nonGaussian distribution of the returns, we randomized the time order of the returns and reevaluated the exponent values. We find that, for the randomized time series, the exponent values ∼0.5 for both the returns and volatilities.

↵ See SI Appendix for the P values from the KS tests. The confidence bounds in Fig. 3A and B show that the deviations in the tails are consistent with expected fluctuations.

↵ Refer to the SI Appendix for description of these and related statistical methods.

↵ However, in ref. 56, R. K. Pan and S. Sinha have analyzed highfrequency tickbytick data for the Indian stock market and found that the cumulative distribution has a tail described by the power law with an exponent ∼3 contrary to the findings in ref. 50.

↵ Technically, P(t_{i}) is the risk neutral measure, but should approximate the true probability in the absence of significant hedging demand. This implies the best forecast of the next price is the current price. In fact, the current price is the best forecast of the settlement value. In context, this is Fama's weak form efficiency with a zero expected return (27). A continuous arbitrage opportunity built into the IEM restricts the riskfree rate to zero. Specifically, the “unit portfolio” of both (or all three) contracts is risk free and can always be traded for $1 cash and vice versa. Cash accounts earn zero interest. Since the aggregate portfolio is also risk free, it earns a zero return and, hence, the returns to aggregate risk factors are zero. That is, all assets should earn the riskfree rate, in this case, 0. Pricing contingent claims with zero aggregate risk at expected value results from a simple extension of refs. 40 and 41.

↵ We have assumed that ɛ has mean zero. One might, instead, assume that the mean is not zero and attempt to estimate it as well. In Eq. 11, however, both the μ and γ effectively scale the jump sizes relative to the remaining time controlling the speed of convergence. As a result, they prove very difficult to identify independently without inordinate amounts of data. Preliminary analysis indicates a correspondence between the μ and γ estimates, where the speed of convergence weighs relatively more heavily on one parameter or the other. Pairs of estimates appear to explain the data equally. Here, we choose to model mean zero noise and let γ reflect the speed of convergence. We leave further exploration of the μ – γ relationship to future research.

This article contains supporting information online at www.pnas.org/cgi/content/full/0805037106/DCSupplemental.
 © 2009 by The National Academy of Sciences of the USA
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