| Panel A. Level . | Panel B. First-order difference . | |||||||
|---|---|---|---|---|---|---|---|---|
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S)·102 . | ΔVOL . | ΔSKEW . | ΔKURT . | |
| Mean | 7.947 | 0.160 | −2.017 | 12.815 | 0.056 | 0.000 | 0.000 | 0.006 |
| Std. dev. | 0.236 | 0.101 | 0.901 | 8.836 | 1.225 | 0.039 | 0.519 | 5.420 |
| 5th pct. | 7.625 | 0.075 | −3.795 | 4.581 | −1.743 | −0.047 | −0.835 | −7.630 |
| 25th pct. | 7.769 | 0.102 | −2.479 | 6.476 | −0.314 | −0.014 | −0.250 | −1.730 |
| Median | 7.928 | 0.135 | −1.799 | 9.900 | 0.079 | −0.001 | −0.002 | −0.043 |
| 75th pct. | 8.087 | 0.186 | −1.331 | 16.131 | 0.574 | 0.011 | 0.258 | 1.718 |
| 95th pct. | 8.398 | 0.316 | −0.952 | 32.089 | 1.514 | 0.048 | 0.808 | 8.061 |
| Skewness | 0.455 | 4.012 | −1.166 | 1.841 | −1.245 | 2.302 | −0.231 | 0.245 |
| Kurtosis | 2.402 | 28.577 | 4.451 | 7.124 | 24.386 | 34.108 | 6.880 | 12.232 |
| # of obs. | 1,528 | 1,528 | 1,528 | 1,528 | 1,527 | 1,527 | 1,527 | 1,527 |
| Panel A. Level . | Panel B. First-order difference . | |||||||
|---|---|---|---|---|---|---|---|---|
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S)·102 . | ΔVOL . | ΔSKEW . | ΔKURT . | |
| Mean | 7.947 | 0.160 | −2.017 | 12.815 | 0.056 | 0.000 | 0.000 | 0.006 |
| Std. dev. | 0.236 | 0.101 | 0.901 | 8.836 | 1.225 | 0.039 | 0.519 | 5.420 |
| 5th pct. | 7.625 | 0.075 | −3.795 | 4.581 | −1.743 | −0.047 | −0.835 | −7.630 |
| 25th pct. | 7.769 | 0.102 | −2.479 | 6.476 | −0.314 | −0.014 | −0.250 | −1.730 |
| Median | 7.928 | 0.135 | −1.799 | 9.900 | 0.079 | −0.001 | −0.002 | −0.043 |
| 75th pct. | 8.087 | 0.186 | −1.331 | 16.131 | 0.574 | 0.011 | 0.258 | 1.718 |
| 95th pct. | 8.398 | 0.316 | −0.952 | 32.089 | 1.514 | 0.048 | 0.808 | 8.061 |
| Skewness | 0.455 | 4.012 | −1.166 | 1.841 | −1.245 | 2.302 | −0.231 | 0.245 |
| Kurtosis | 2.402 | 28.577 | 4.451 | 7.124 | 24.386 | 34.108 | 6.880 | 12.232 |
| # of obs. | 1,528 | 1,528 | 1,528 | 1,528 | 1,527 | 1,527 | 1,527 | 1,527 |
Notes: This table provides summary statistics for the daily model-free implied moment estimates derived using the BKM estimators, without applying any truncation error treatment. S, VOL, SKEW, and KURT denote the underlying price, implied volatility, skewness, and kurtosis, respectively. The option prices are approximated for a time to maturity of seven calendar days from daily implied volatility surfaces. Panels A and B present the summary statistics for the levels and first-order differences, respectively.
| Panel A. Level . | Panel B. First-order difference . | |||||||
|---|---|---|---|---|---|---|---|---|
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S)·102 . | ΔVOL . | ΔSKEW . | ΔKURT . | |
| Mean | 7.947 | 0.160 | −2.017 | 12.815 | 0.056 | 0.000 | 0.000 | 0.006 |
| Std. dev. | 0.236 | 0.101 | 0.901 | 8.836 | 1.225 | 0.039 | 0.519 | 5.420 |
| 5th pct. | 7.625 | 0.075 | −3.795 | 4.581 | −1.743 | −0.047 | −0.835 | −7.630 |
| 25th pct. | 7.769 | 0.102 | −2.479 | 6.476 | −0.314 | −0.014 | −0.250 | −1.730 |
| Median | 7.928 | 0.135 | −1.799 | 9.900 | 0.079 | −0.001 | −0.002 | −0.043 |
| 75th pct. | 8.087 | 0.186 | −1.331 | 16.131 | 0.574 | 0.011 | 0.258 | 1.718 |
| 95th pct. | 8.398 | 0.316 | −0.952 | 32.089 | 1.514 | 0.048 | 0.808 | 8.061 |
| Skewness | 0.455 | 4.012 | −1.166 | 1.841 | −1.245 | 2.302 | −0.231 | 0.245 |
| Kurtosis | 2.402 | 28.577 | 4.451 | 7.124 | 24.386 | 34.108 | 6.880 | 12.232 |
| # of obs. | 1,528 | 1,528 | 1,528 | 1,528 | 1,527 | 1,527 | 1,527 | 1,527 |
| Panel A. Level . | Panel B. First-order difference . | |||||||
|---|---|---|---|---|---|---|---|---|
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S)·102 . | ΔVOL . | ΔSKEW . | ΔKURT . | |
| Mean | 7.947 | 0.160 | −2.017 | 12.815 | 0.056 | 0.000 | 0.000 | 0.006 |
| Std. dev. | 0.236 | 0.101 | 0.901 | 8.836 | 1.225 | 0.039 | 0.519 | 5.420 |
| 5th pct. | 7.625 | 0.075 | −3.795 | 4.581 | −1.743 | −0.047 | −0.835 | −7.630 |
| 25th pct. | 7.769 | 0.102 | −2.479 | 6.476 | −0.314 | −0.014 | −0.250 | −1.730 |
| Median | 7.928 | 0.135 | −1.799 | 9.900 | 0.079 | −0.001 | −0.002 | −0.043 |
| 75th pct. | 8.087 | 0.186 | −1.331 | 16.131 | 0.574 | 0.011 | 0.258 | 1.718 |
| 95th pct. | 8.398 | 0.316 | −0.952 | 32.089 | 1.514 | 0.048 | 0.808 | 8.061 |
| Skewness | 0.455 | 4.012 | −1.166 | 1.841 | −1.245 | 2.302 | −0.231 | 0.245 |
| Kurtosis | 2.402 | 28.577 | 4.451 | 7.124 | 24.386 | 34.108 | 6.880 | 12.232 |
| # of obs. | 1,528 | 1,528 | 1,528 | 1,528 | 1,527 | 1,527 | 1,527 | 1,527 |
Notes: This table provides summary statistics for the daily model-free implied moment estimates derived using the BKM estimators, without applying any truncation error treatment. S, VOL, SKEW, and KURT denote the underlying price, implied volatility, skewness, and kurtosis, respectively. The option prices are approximated for a time to maturity of seven calendar days from daily implied volatility surfaces. Panels A and B present the summary statistics for the levels and first-order differences, respectively.
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