| Panel A. No stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | − | − | − | Δln(S) | 1.000 | − | − | − |
| VOL | 0.037 | 1.000 | − | − | ΔVOL | −0.767 | 1.000 | − | − |
| SKEW | −0.355 | 0.129 | 1.000 | − | ΔSKEW | −0.017 | −0.126 | 1.000 | − |
| KURT | 0.415 | −0.116 | −0.966 | 1.000 | ΔKURT | 0.021 | 0.074 | −0.942 | 1.000 |
| Panel A. No stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | − | − | − | Δln(S) | 1.000 | − | − | − |
| VOL | 0.037 | 1.000 | − | − | ΔVOL | −0.767 | 1.000 | − | − |
| SKEW | −0.355 | 0.129 | 1.000 | − | ΔSKEW | −0.017 | −0.126 | 1.000 | − |
| KURT | 0.415 | −0.116 | −0.966 | 1.000 | ΔKURT | 0.021 | 0.074 | −0.942 | 1.000 |
| Panel B. 0% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.035 | 1.000 | – | – | ΔVOL | −0.767 | 1.000 | – | – |
| SKEW | −0.340 | 0.142 | 1.000 | – | ΔSKEW | −0.015 | −0.123 | 1.000 | – |
| KURT | 0.383 | −0.146 | −0.971 | 1.000 | ΔKURT | 0.028 | 0.060 | −0.945 | 1.000 |
| Panel B. 0% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.035 | 1.000 | – | – | ΔVOL | −0.767 | 1.000 | – | – |
| SKEW | −0.340 | 0.142 | 1.000 | – | ΔSKEW | −0.015 | −0.123 | 1.000 | – |
| KURT | 0.383 | −0.146 | −0.971 | 1.000 | ΔKURT | 0.028 | 0.060 | −0.945 | 1.000 |
| Panel C. 25% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.029 | 1.000 | – | – | ΔVOL | −0.769 | 1.000 | – | – |
| SKEW | −0.278 | 0.188 | 1.000 | – | ΔSKEW | −0.017 | −0.142 | 1.000 | – |
| KURT | 0.309 | −0.221 | −0.976 | 1.000 | ΔKURT | 0.018 | 0.094 | −0.954 | 1.000 |
| Panel C. 25% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.029 | 1.000 | – | – | ΔVOL | −0.769 | 1.000 | – | – |
| SKEW | −0.278 | 0.188 | 1.000 | – | ΔSKEW | −0.017 | −0.142 | 1.000 | – |
| KURT | 0.309 | −0.221 | −0.976 | 1.000 | ΔKURT | 0.018 | 0.094 | −0.954 | 1.000 |
| Panel D. 50% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.025 | 1.000 | – | – | ΔVOL | −0.771 | 1.000 | – | – |
| SKEW | −0.235 | 0.214 | 1.000 | – | ΔSKEW | −0.030 | −0.146 | 1.000 | – |
| KURT | 0.256 | −0.269 | −0.970 | 1.000 | ΔKURT | 0.026 | 0.107 | −0.949 | 1.000 |
| Panel D. 50% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.025 | 1.000 | – | – | ΔVOL | −0.771 | 1.000 | – | – |
| SKEW | −0.235 | 0.214 | 1.000 | – | ΔSKEW | −0.030 | −0.146 | 1.000 | – |
| KURT | 0.256 | −0.269 | −0.970 | 1.000 | ΔKURT | 0.026 | 0.107 | −0.949 | 1.000 |
| Panel E. 75% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.021 | 1.000 | – | – | ΔVOL | −0.774 | 1.000 | – | – |
| SKEW | −0.198 | 0.225 | 1.000 | – | ΔSKEW | −0.056 | −0.127 | 1.000 | – |
| KURT | 0.211 | −0.302 | −0.961 | 1.000 | ΔKURT | 0.055 | 0.091 | −0.940 | 1.000 |
| Panel E. 75% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.021 | 1.000 | – | – | ΔVOL | −0.774 | 1.000 | – | – |
| SKEW | −0.198 | 0.225 | 1.000 | – | ΔSKEW | −0.056 | −0.127 | 1.000 | – |
| KURT | 0.211 | −0.302 | −0.961 | 1.000 | ΔKURT | 0.055 | 0.091 | −0.940 | 1.000 |
| Panel F. 100% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.017 | 1.000 | – | – | ΔVOL | −0.783 | 1.000 | – | – |
| SKEW | −0.177 | 0.277 | 1.000 | – | ΔSKEW | −0.179 | 0.011 | 1.000 | – |
| KURT | 0.210 | −0.335 | −0.953 | 1.000 | ΔKURT | 0.151 | −0.004 | −0.920 | 1.000 |
| Panel F. 100% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.017 | 1.000 | – | – | ΔVOL | −0.783 | 1.000 | – | – |
| SKEW | −0.177 | 0.277 | 1.000 | – | ΔSKEW | −0.179 | 0.011 | 1.000 | – |
| KURT | 0.210 | −0.335 | −0.953 | 1.000 | ΔKURT | 0.151 | −0.004 | −0.920 | 1.000 |
Notes: This table presents the correlation coefficient estimates between the levels and first-order differences of the daily underlying log price and the implied moment estimates. S, VOL, SKEW, and KURT represent the underlying price and the implied volatility, skewness, and kurtosis estimates, respectively. Δ denotes the first-order difference operator. Panel A provides the correlation coefficient estimates for the no stabilization case, while Panels B–F present the estimates for DStab at intensity levels of 0%, 25%, 50%, 75%, and 100%, respectively.
| Panel A. No stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | − | − | − | Δln(S) | 1.000 | − | − | − |
| VOL | 0.037 | 1.000 | − | − | ΔVOL | −0.767 | 1.000 | − | − |
| SKEW | −0.355 | 0.129 | 1.000 | − | ΔSKEW | −0.017 | −0.126 | 1.000 | − |
| KURT | 0.415 | −0.116 | −0.966 | 1.000 | ΔKURT | 0.021 | 0.074 | −0.942 | 1.000 |
| Panel A. No stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | − | − | − | Δln(S) | 1.000 | − | − | − |
| VOL | 0.037 | 1.000 | − | − | ΔVOL | −0.767 | 1.000 | − | − |
| SKEW | −0.355 | 0.129 | 1.000 | − | ΔSKEW | −0.017 | −0.126 | 1.000 | − |
| KURT | 0.415 | −0.116 | −0.966 | 1.000 | ΔKURT | 0.021 | 0.074 | −0.942 | 1.000 |
| Panel B. 0% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.035 | 1.000 | – | – | ΔVOL | −0.767 | 1.000 | – | – |
| SKEW | −0.340 | 0.142 | 1.000 | – | ΔSKEW | −0.015 | −0.123 | 1.000 | – |
| KURT | 0.383 | −0.146 | −0.971 | 1.000 | ΔKURT | 0.028 | 0.060 | −0.945 | 1.000 |
| Panel B. 0% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.035 | 1.000 | – | – | ΔVOL | −0.767 | 1.000 | – | – |
| SKEW | −0.340 | 0.142 | 1.000 | – | ΔSKEW | −0.015 | −0.123 | 1.000 | – |
| KURT | 0.383 | −0.146 | −0.971 | 1.000 | ΔKURT | 0.028 | 0.060 | −0.945 | 1.000 |
| Panel C. 25% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.029 | 1.000 | – | – | ΔVOL | −0.769 | 1.000 | – | – |
| SKEW | −0.278 | 0.188 | 1.000 | – | ΔSKEW | −0.017 | −0.142 | 1.000 | – |
| KURT | 0.309 | −0.221 | −0.976 | 1.000 | ΔKURT | 0.018 | 0.094 | −0.954 | 1.000 |
| Panel C. 25% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.029 | 1.000 | – | – | ΔVOL | −0.769 | 1.000 | – | – |
| SKEW | −0.278 | 0.188 | 1.000 | – | ΔSKEW | −0.017 | −0.142 | 1.000 | – |
| KURT | 0.309 | −0.221 | −0.976 | 1.000 | ΔKURT | 0.018 | 0.094 | −0.954 | 1.000 |
| Panel D. 50% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.025 | 1.000 | – | – | ΔVOL | −0.771 | 1.000 | – | – |
| SKEW | −0.235 | 0.214 | 1.000 | – | ΔSKEW | −0.030 | −0.146 | 1.000 | – |
| KURT | 0.256 | −0.269 | −0.970 | 1.000 | ΔKURT | 0.026 | 0.107 | −0.949 | 1.000 |
| Panel D. 50% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.025 | 1.000 | – | – | ΔVOL | −0.771 | 1.000 | – | – |
| SKEW | −0.235 | 0.214 | 1.000 | – | ΔSKEW | −0.030 | −0.146 | 1.000 | – |
| KURT | 0.256 | −0.269 | −0.970 | 1.000 | ΔKURT | 0.026 | 0.107 | −0.949 | 1.000 |
| Panel E. 75% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.021 | 1.000 | – | – | ΔVOL | −0.774 | 1.000 | – | – |
| SKEW | −0.198 | 0.225 | 1.000 | – | ΔSKEW | −0.056 | −0.127 | 1.000 | – |
| KURT | 0.211 | −0.302 | −0.961 | 1.000 | ΔKURT | 0.055 | 0.091 | −0.940 | 1.000 |
| Panel E. 75% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.021 | 1.000 | – | – | ΔVOL | −0.774 | 1.000 | – | – |
| SKEW | −0.198 | 0.225 | 1.000 | – | ΔSKEW | −0.056 | −0.127 | 1.000 | – |
| KURT | 0.211 | −0.302 | −0.961 | 1.000 | ΔKURT | 0.055 | 0.091 | −0.940 | 1.000 |
| Panel F. 100% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.017 | 1.000 | – | – | ΔVOL | −0.783 | 1.000 | – | – |
| SKEW | −0.177 | 0.277 | 1.000 | – | ΔSKEW | −0.179 | 0.011 | 1.000 | – |
| KURT | 0.210 | −0.335 | −0.953 | 1.000 | ΔKURT | 0.151 | −0.004 | −0.920 | 1.000 |
| Panel F. 100% stabilization . | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Level . | First-order difference . | ||||||||
| ln(S) . | VOL . | SKEW . | KURT . | Δln(S) . | ΔVOL . | ΔSKEW . | ΔKURT . | ||
| ln(S) | 1.000 | – | – | – | Δln(S) | 1.000 | – | – | – |
| VOL | 0.017 | 1.000 | – | – | ΔVOL | −0.783 | 1.000 | – | – |
| SKEW | −0.177 | 0.277 | 1.000 | – | ΔSKEW | −0.179 | 0.011 | 1.000 | – |
| KURT | 0.210 | −0.335 | −0.953 | 1.000 | ΔKURT | 0.151 | −0.004 | −0.920 | 1.000 |
Notes: This table presents the correlation coefficient estimates between the levels and first-order differences of the daily underlying log price and the implied moment estimates. S, VOL, SKEW, and KURT represent the underlying price and the implied volatility, skewness, and kurtosis estimates, respectively. Δ denotes the first-order difference operator. Panel A provides the correlation coefficient estimates for the no stabilization case, while Panels B–F present the estimates for DStab at intensity levels of 0%, 25%, 50%, 75%, and 100%, respectively.
This PDF is available to Subscribers Only
View Article Abstract & Purchase OptionsFor full access to this pdf, sign in to an existing account, or purchase an annual subscription.
