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Inferring the Forward Looking Equity Risk Premium from Derivative Prices


Author Info

  • Bhar Ramaprasad

    (The University of New South Wales)

  • Chiarella Carl

    (University of Technology, Sydney, Australia)

  • Runggaldier Wolfgang J.

    (University of Padova, Italy)


This paper considers the measurement of the equity risk premium in financial markets from a new perspective that picks up on a suggestion from Merton (1980) to use implied volatility of options on a market portfolio as a direct ‘ex-ante’ estimate for market variance, and hence the risk premium. Here the time variation of the unobserved risk premium is modelled by a system of stochastic differential equations connected by arbitrage arguments between the spot equity market, the index futures and options on index futures. We motivate and analyse a mean-reverting form for the dynamics of the risk premium. Since the risk premium is not directly observable, information about its time varying conditional distribution is extracted using an unobserved component state space formulation of the system and Kalman filtering methodology. In order to cater for the time variation of volatility we use the option implied volatility in the dynamic equations for the index and its derivatives. This quantity is in a sense treated as a signal that impounds the market’s ‘ex-ante’, forward looking, view on the equity risk premium. The results using monthly U.S. market data over the period January 1995 to June 2003 are presented and the model fit is found to be statistically significant using a number of measures. Comparisons with ex-post returns indicate that such historical measures may be understating the market risk premium.

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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 8 (2004)
Issue (Month): 1 (March)
Pages: 1-26

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Handle: RePEc:bpj:sndecm:v:8:y:2004:i:1:n:3

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Cited by:
  1. Ramaprasad Bhar, 2010. "Stochastic Filtering With Applications In Finance:," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., number 7736.
  2. Bhar, Ramaprasad & Hamori, Shigeyuki, 2007. "Co-movement in the price of risk of aggregate equity markets," Economic Systems, Elsevier, Elsevier, vol. 31(3), pages 256-271, September.
  3. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 191, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer, Springer, vol. 11(1), pages 79-105, March.
  5. Ren-Her Wang & John Aston & Cheng-Der Fuh, 2010. "The Role of Additional Information in Option Pricing: Estimation Issues for the State Space Model," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 36(4), pages 283-307, December.
  6. Bhar, Ramaprasad & Nikolova, Biljana, 2013. "Measuring the interconnectedness of financial institutions," Economic Systems, Elsevier, Elsevier, vol. 37(1), pages 17-29.


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