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arXiv · 2607.08500

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

Kenichiro Shiraya·Tomohisa Yamakami·Akira Yamazaki
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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.

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Kenichiro Shiraya, Tomohisa Yamakami, Akira Yamazaki. 2026-07-09. Estimating the Stochastic Discount Factor from Option Prices and Predicting the Equity Premium. https://arxiv.org/abs/2607.08500

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