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A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

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  • Shackleton, Mark B.
  • Taylor, Stephen J.
  • Yu, Peng

Abstract

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 34 (2010)
Issue (Month): 11 (November)
Pages: 2678-2693

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Handle: RePEc:eee:jbfina:v:34:y:2010:i:11:p:2678-2693

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Web page: http://www.elsevier.com/locate/jbf

Related research

Keywords: ARCH models Density forecasts Index options Risk-neutral densities Risk-transformations;

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Cited by:
  1. Baule, Rainer & Korn, Olaf & Saßning, Sven, 2013. "Which beta is best? On the information content of option-implied betas," CFR Working Papers 13-11, University of Cologne, Centre for Financial Research (CFR).
  2. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
  3. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2009. "Option-implied preferences adjustments, density forecasts, and the equity risk premium," Spanish Economic Review, Springer, vol. 11(2), pages 141-164, June.
  4. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, School of Economics and Management, University of Aarhus.
  5. Takkabutr, Nattapol, 2013. "Option-Implied Risk Aversion Anomalies: Evidence From Japanese Market," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 54(2), pages 137-157, December.
  6. Belén Nieto & Gonzalo Rubio, 2007. "Measuring time-varying economic fears with consumption-based stochastic discount factors," Economics Working Papers 1029, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2007.
  7. de Vincent-Humphreys, Rupert & Noss, Joseph, 2012. "Estimating probability distributions of future asset prices: empirical transformations from option-implied risk-neutral to real-world density functions," Bank of England working papers 455, Bank of England.
  8. Kempf, Alexander & Korn, Olaf & Saßning, Sven, 2014. "Portfolio optimization using forward-looking information," CFR Working Papers 11-10 [rev.], University of Cologne, Centre for Financial Research (CFR).

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