Estimating a Volatility-Scaled Discount Factor from S&P 500 Options

Summary

The paper develops a stochastic discount factor (SDF) that is scaled by time-varying volatility and estimated using information implied by S&P 500 option prices. The aim is to recover market participants’ forward-looking expectations while reducing the effect of observation noise. The estimated SDF has a non-monotonic shape, with a hump on the shallow put side that becomes more distinctly W-shaped at longer maturities. The results identify maturity as a factor in the strength of the central hump.

The authors explain that stochastic volatility with a constant market price of risk can account for this shape. They also use the estimated SDF to derive an equity premium and report stronger out-of-sample predictive performance than existing benchmarks, including the Martin bounds. The document does not provide details on the sample period, implementation choices, or the size and statistical significance of the predictive gains, so the summary supports understanding the proposed approach but not assessing its robustness independently.

Key ideas

• The proposed SDF scales option-implied information by time-varying volatility.
• Its estimated shape is non-monotonic, with a shallow-put-side hump that becomes more W-shaped at longer maturities.
• Stochastic volatility under a constant market price of risk offers a theoretical explanation for the observed shape.
• The resulting equity premium is reported to predict out of sample better than benchmarks such as the Martin bounds.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.