A significant amount of research has been conducted on the volatility risk premium (VRP). Reference [1] contributes to this literature by linking the VRP to the parameters of the Heston model. The Heston model is a widely used stochastic volatility model that captures time-varying volatility and mean-reverting dynamics.
Unlike previous studies, the authors do not rely on a theoretical model to estimate the VRP, but instead use returns from variance-related financial instruments, including variance swaps, VIX futures, and straddles, as proxies, examined over 7- and 30-day horizons. They pointed out,
The economic magnitude is substantial. A one-standard-deviation increase in v0 is associated with approximately 730 basis points lower next-day returns for the 7-day variance swap. This confirms that the current level of market variance is the primary driver of near-term VRP: when variance is elevated, the compensation demanded by investors for bearing variance risk increases, depressing expected returns on long-volatility positions…
This pattern supports Hypothesis 2: greater uncertainty about future variance dynamics leads to larger risk premia and more negative expected returns. The slightly weaker significance for 30-day straddles may reflect the attenuation of uncertainty effects at longer horizons, where the convex payoff structure provides some natural hedging against variance fluctuations…
At the 30-day horizon, the significance of κ diminishes substantially. For variance swaps and straddles, coefficients become statistically indistinguishable from zero. Only for VIX futures does κ retain marginal significance. This differential pattern across maturities—significance at 7 days but not at 30 days—is precisely what Hypothesis 3 predicts and provides validation of the underlying economic mechanism.
In summary, the results show that the initial variance level is a strong negative predictor across all cases, volatility of volatility is also negative and robust, mean reversion is relevant only in the short term, and long-run parameters are largely irrelevant.
These findings suggest that the VRP is primarily driven by current volatility levels and uncertainty rather than long-term factors, providing useful insights for portfolio and risk management.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Han, C.-H., & Wang, K. (2026), Variance Risk Premia under Volatility Models, Review of Quantitative Finance and Accounting.
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