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

Kenichiro Shiraya, Tomohisa Yamakami and Akira Yamazaki
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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

No CARF-F-629, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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

Pages: 31
Date: 2026-07
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf629

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