Out-of-sample pricing performance
| <Panel A> MAE | |||||
|---|---|---|---|---|---|
| In-sample | 1-day | 3-day | 5-day | 7-day | |
| BS | 0.2907 | 0.3133 | 0.3369 | 0.3632 | 0.3964 |
| A1 | 0.2307 | 0.2804 | 0.2909 | 0.3420 | 0.4095 |
| A2 | 0.1061 | 0.2634 | 0.2639 | 0.3923 | 0.5117 |
| R1 | 0.1741 | 0.2650 | 0.2945 | 0.3650 | 0.4493 |
| R2 | 0.1267 | 0.3690 | 0.3552 | 0.5437 | 0.7199 |
| SV | 0.0578 | 0.2031 | 0.2321 | 0.3420 | 0.4121 |
| SVJ | 0.0524 | 0.1622 | 0.2069 | 0.2600 | 0.3024 |
| <Panel A> MAE | |||||
|---|---|---|---|---|---|
| In-sample | 1-day | 3-day | 5-day | 7-day | |
| BS | 0.2907 | 0.3133 | 0.3369 | 0.3632 | 0.3964 |
| A1 | 0.2307 | 0.2804 | 0.2909 | 0.3420 | 0.4095 |
| A2 | 0.1061 | 0.2634 | 0.2639 | 0.3923 | 0.5117 |
| R1 | 0.1741 | 0.2650 | 0.2945 | 0.3650 | 0.4493 |
| R2 | 0.1267 | 0.3690 | 0.3552 | 0.5437 | 0.7199 |
| SV | 0.0578 | 0.2031 | 0.2321 | 0.3420 | 0.4121 |
| SVJ | 0.0524 | 0.1622 | 0.2069 | 0.2600 | 0.3024 |
| <Panel B> MSE | |||||
|---|---|---|---|---|---|
| In-sample | 1-day | 3-day | 5-day | 7-day | |
| BS | 0.2179 | 0.2915 | 0.3696 | 0.4826 | 0.6190 |
| A1 | 0.1848 | 0.3239 | 0.3743 | 0.5333 | 0.7581 |
| A2 | 0.0649 | 0.6560 | 0.4469 | 0.8903 | 1.2760 |
| R1 | 0.1248 | 0.3058 | 0.3879 | 0.5933 | 0.8651 |
| R2 | 0.0850 | 2.8752 | 1.7969 | 3.4508 | 5.4082 |
| SV | 0.0275 | 0.3689 | 0.3068 | 0.7986 | 0.9908 |
| SVJ | 0.0268 | 0.1254 | 0.1900 | 0.3146 | 0.3900 |
| <Panel B> MSE | |||||
|---|---|---|---|---|---|
| In-sample | 1-day | 3-day | 5-day | 7-day | |
| BS | 0.2179 | 0.2915 | 0.3696 | 0.4826 | 0.6190 |
| A1 | 0.1848 | 0.3239 | 0.3743 | 0.5333 | 0.7581 |
| A2 | 0.0649 | 0.6560 | 0.4469 | 0.8903 | 1.2760 |
| R1 | 0.1248 | 0.3058 | 0.3879 | 0.5933 | 0.8651 |
| R2 | 0.0850 | 2.8752 | 1.7969 | 3.4508 | 5.4082 |
| SV | 0.0275 | 0.3689 | 0.3068 | 0.7986 | 0.9908 |
| SVJ | 0.0268 | 0.1254 | 0.1900 | 0.3146 | 0.3900 |
Note(s): This table reports the out-of-sample pricing errors of each option pricing model across different forecast horizons. Each model is estimated on a daily basis, and the out-of-sample pricing error is computed as the difference between the market option price and the model-implied option price using the parameters estimated on day t to evaluate options at day t + N. MAE denotes the mean absolute error, and MSE denotes the mean squared error. BS refers to the Black and Scholes (1973) model. The A1 model uses the intercept and strike price as independent variables, while the A2 model includes the intercept, strike price, and squared strike price. The R1 model uses the intercept and moneyness, while the R2 model includes the intercept, moneyness, and squared moneyness. SV and SVJ refer to the stochastic volatility model and the stochastic volatility with jumps model of Bakshi et al. (1997), respectively