本文探討 SPX 選擇權曲面所隱含的資訊，是否能預測 VIX 選擇權市場中的風險溢酬。由於 VIX 本身即由 SPX 選擇權價格建構而成，本文進一步檢驗 SPX 選擇權曲面中的資訊是否僅反映於 VIX 水準，或亦能預測 VIX 選擇權的未來 delta-hedged returns。本文建構六個 VIX 選擇權價性區間下的一個月與六個月 bucket-month delta-hedged returns，並測試六項 SPX option-implied predictors，包括 CBOE SKEW、SVIX2、SPX variance risk premium，以及 Bakshi–Kapadia–Madan risk-neutral variance、skewness 與 kurtosis。實證設計進一步控制 VIX、VVIX、VIX futures basis、term-structure slope 與落後一期 VIX futures return，並於各預測期間內採用 Benjamini–Hochberg 與 Holm–Bonferroni 方法處理多重檢定問題。實證結果顯示，SPX 選擇權資訊對 VIX 選擇權風險溢酬的預測力並非全面存在，而是集中於六個月期間下的 BKM risk-neutral skewness。相較之下，CBOE SKEW 與 SPX variance risk premium 在控制 VIX 市場狀態後不再保留穩定的增量預測力。進一步透過將 BKM risk-neutral skewness 與 CBOE SKEW 指數同時納入迴歸模型的 horse-race specification，本文發現 BKM risk-neutral skewness 所包含的資訊並非 CBOE SKEW 指數可以完全概括。整體而言，本文指出 SPX 選擇權曲面的分配形狀資訊，特別是 model-free risk-neutral skewness，對 VIX 選擇權風險溢酬具有增量預測內容。

I ask whether information in the SPX option surface forecasts risk premia in the VIX option market, using bucket-month delta-hedged returns on VIX options across six moneyness buckets and two horizons. Because VIX options are among the most direct traded claims on equity-market volatility, identifying what predicts their risk premia helps clarify how information in the equity-option surface is transmitted into the volatility-derivatives market. I find that the predictive content of SPX option-implied information is concentrated in model-free risk-neutral skewness rather than in standard off-the-shelf summary indices, and that this concentration survives a set of in-sample robustness checks and construction-sensitivity tests, including a horse-race specification that jointly includes BKM risk-neutral skewness and the CBOE SKEW index.

The empirical design follows Park (2015), extended to a hold-to-expiration setting in which the terminal option value coincides with the SOQ-settled payoff and the maturity-matched VIX futures contract is the static hedging instrument. Six SPX option-implied predictors are tested under Benjamini–Hochberg and Holm–Bonferroni correction within horizon-specific 36-test families, with progressively richer vol-market state controls.

CBOE SKEW and the variance risk premium lose significance once VIX, VVIX, and the VIX futures term structure are jointly controlled; BKM risk-neutral skewness retains stable BH-significant slopes in three middle-moneyness buckets, with magnitudes that remain stable across sub-period splits, with March 2020 excluded, under NW(12) inference, under open-interest weighting, and in the horse-race specification against the CBOE SKEW index. The single Holm-significant cell, SVIX2(180d) × OTM put, reflects a numerical amplification associated with its 0.90 correlation with the VIX level; the vol-state-orthogonal component of SVIX2 retains a smaller robust effect concentrated in the post-COVID sub-period.

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