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

Battle Count: 68

The paper provides a robust framework for estimating the equity premium from option-implied data with demonstrated out-of-sample predictive power, particularly at longer horizons (120-360 days). The TVS SDF outperforms Martin bounds and historical averages. This is directly relevant for systematic equity premium timing strategies, volatility risk premium harvesting, and derivatives-based risk management. However, the wide confidence intervals and limited short-term predictive power reduce immediate practical applicability for high-frequency trading. The framework is more suited for medium-to-long horizon allocation decisions and risk assessment.

The methodology involves multiple complex components: (1) extracting implied spot rates, interest rates, and dividend yields from option prices using box-spread and Theil-Sen estimators; (2) computing variance swap rates via Carr-Madan spanning formula with numerical integration; (3) estimating piecewise polynomial SDFs via GMM with HJ distance minimization; (4) adjusting SDF for discount bond price consistency; (5) computing equity premium via Carr-Madan formula; (6) expanding window out-of-sample estimation. The numerical integration, GMM optimization, and bootstrap procedures require careful implementation. The paper provides detailed appendices for the estimation procedures.

The paper uses publicly available Option Metrics data for S&P 500 options. The methodology is well-documented with detailed equations, estimation procedures, and numerical integration schemes in appendices. However, no code or repository is explicitly provided. The GMM estimation with HJ distance minimization and the specific strike selection methodology are described in sufficient detail for replication, but the exact implementation of the expanding window estimation and bootstrap procedures would require careful reimplementation.