Modeling volatility in prediction markets

ABSTRACT

There is significant experimental evidence that prediction markets are efficient mechanisms for aggregating information and are more accurate in forecasting events than traditional forecasting methods, such as polls. Interpretation of prediction market prices as probabilities has been extensively studied in the literature. However there is little research on the volatility of prediction market prices. Given that volatility is fundamental in estimating significance of price movements, it is important to have a better understanding of the volatility of the contract prices.

This paper presents a model of a prediction market with binary payoff on a competitive event involving two parties. In our model, each party has a latent underlying "ability" process that describes its ability to win and evolves as an Ito diffusion. We show that, if the prediction market for this event is efficient and unbiased, the price of the corresponding contract also follows a diffusion and its instantaneous volatility is a function of the current contract price and its time to expiration. In the experimental section, we validate our model on a set of InTrade prediction markets and show that our model is consistent with the observed volatility of contract returns. Our model also outperforms existing volatility models in predicting future contract volatility from historical price data. To demonstrate the practical value of our model, we apply it to pricing options on prediction market contracts, such as those recently introduced by InTrade. Other potential applications of this model include detection of significant market moves and improving forecast standard errors.

REFERENCES

• 1: N. Archak and P.G. Ipeirotis. Modeling volatility in prediction markets, Sept. 2008. Working Paper.
• 2: A. Bera and M. Higgins. ARCH models: Properties, estimation and testing. Journal of Economic Surveys, 7(4):305--366, 1993.
• 3: J. Berg, R. Forsythe, F. Nelson, and T. Rietz. Results from a dozen years of election futures markets research, 2003. Working Draft, The Handbook of Experimental Economics Results.
• 4: Joyce E. Berg , Thomas A. Rietz, Prediction Markets as Decision Support Systems, Information Systems Frontiers, v.5 n.1, p.79-93, January 2003 [doi>10.1023/A:1022002107255]
• 5: F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637--654, 1973.
• 6: T. Bollerslev. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31:307--327, 1986.
• 7: K.-Y. Chen and C. Plott. Information aggregation mechanisms: Concept, design and field implementation for a sales forecasting problem, 2002.
• 8: M. Keith Chen , Jonathan E. Ingersoll , Edward H. Kaplan, Modeling a Presidential Prediction Market, Management Science, v.54 n.8, p.1381-1394, August 2008 [doi>10.1287/mnsc.1080.0872]
• 9: B. Cowgill, J. Wolfers, and E. Zitzewitz. Using prediction markets to track information flows: Evidence from Google, 2008. Working Paper.
• 10: R. Engle and A. Patton. What good is a volatility model? Quantitative Finance, 1(2):237--245, Feb. 2001.
• 11: R.F. Engle. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica, 50(4):987--1008, July 1982.
• 12: R. Forsythe, F. Nelson, G.R. Neumann, and J. Wright. Anatomy of an experimental political stock market. American Economic Review, 82(5):1142--61, December 1992.
• 13: HSX. Hollywood stock exchange traders hit 80% of oscar nominations for the 80th annual academy awards. Available at http://www.hsx.com/about/press/080123.htm, 2008.
• 14: A. Leigh and J. Wolfers. Competing approaches to forecasting elections: Economic models, opinion polling and prediction markets. The Economic Record, 82(258):325--340, 2006.
• 15: S. Luckner, J. Schroder, and C. Slamka. On the forecast accuracy of sports prediction markets. In Negotiation, Auctions, and Market Engineering, volume 2, pages 227--234. Springer Berlin Heidelberg, 2008.
• 16: B. Mandelbrot. The variation of certain speculative prices. Journal of Business, 36(4):394--419, 1963.
• 17: C.F. Manski. Interpreting the predictions of prediction markets. Economic Letters, 91(3):425--429, June 2006.
• 18: R. Merton. Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1):141--183, 1973.
• 19: Bernt Oksendal, Stochastic differential equations (3rd ed.): an introduction with applications, Springer-Verlag New York, Inc., New York, NY, 1992
• 20: D.M. Pennock, S. Debnath, E.J. Glover, and C.L. Giles. Modeling information incorporation in markets with application to detecting and explaining events. In 18th Conference on Uncertainty in Artificial Intelligence (UAI 2002), pages 405--413, 2002.
• 21: E. Servan-Schreiber, J. Wolfers, D.M. Pennock, and B. Galebach. Prediction markets: Does money matter? Electronic Markets, 14(3):243--251, 2004.
• 22: R. Thaler and W. Ziemba. Anomalies: Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives, 2(2):161--174, 1988.
• 23: J. Wolfers and E. Zitzewitz. Prediction markets, 2004. Working Paper.
• 24: J. Wolfers and E. Zitzewitz. Using markets to evaluate policy: The case of the iraq war, 2004. Working Paper.
• 25: J. Wolfers and E. Zitzewitz. Interpreting prediction market prices as probabilities, 2006. Working Paper.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.4 SOCIAL AND BEHAVIORAL SCIENCES
      Subjects: Economics

General Terms:
Economics, Theory

Keywords:
binary option, forecasting, prediction market, volatility