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Estimating the Stochastic Discount Factor from Option Prices and Predicting the Equity Premium

Author

Listed:
  • Kenichiro Shiraya

    (Graduate School of Economics, The University of Tokyo)

  • Tomohisa Yamakami

    (Graduate School of Economics, The University of Tokyo Mizuho-DL Financial Technology Co., Ltd.)

  • Akira Yamazaki

    (Graduate School of Business Administration, Hosei University)

Abstract

This paper proposes a stochastic discount factor (SDF) scaled by time-varying volatility. By utilizing prices and market data implied solely from S\&P 500 options, the proposed framework recovers a stable, non-monotonic SDF that captures the pure forward-looking expectations of market participants while mitigating observation noise. Our empirical analysis reveals that the SDF exhibits a distinctive hump on the shallow put side, which transitions into a more clearly defined W-shape as the time to maturity increases, identifying maturity as a key factor influencing the intensity of the central hump. We show that this structural feature can be theoretically rationalized by stochastic volatility dynamics under a constant market price of risk. The equity premium derived from the time-varying volatility scaled SDF demonstrates superior out-of-sample predictive performance relative to existing benchmarks, such as the Martin bounds. This paper is available at https://arxiv.org/abs/2607.08500Â

Suggested Citation

  • Kenichiro Shiraya & Tomohisa Yamakami & Akira Yamazaki, 2026. "Estimating the Stochastic Discount Factor from Option Prices and Predicting the Equity Premium," CARF F-Series CARF-F-629, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf629
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