From: Upside and downside correlated jump risk premia of currency options and expected returns
 | 1-Month | 3-Month | 6-Month | 12-Month | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
 | CB | CB–ISJ | CB–CSJ | CB–CAJ | CB | CB–ISJ | CB–CSJ | CB–CAJ | CB | CB–ISJ | CB–CSJ | CB–CAJ | CB | CB–ISJ | CB–CSJ | CB–CAJ |
Panel (a): Continuous Part | ||||||||||||||||
\({\mu }_{D}\) | 0.000023 | 0.001735 | − 0.000021 | − 0.001128 | − 0.000032 | 0.001538 | − 0.000243 | − 0.001272 | 0.000011 | 0.004428 | − 0.000516 | − 0.002100 | 0.004191 | 0.004534 | − 0.000329 | − 0.001700 |
 | (0.0005) | (0.0010) | (0.0005) | (0.0003) | (0.0002) | (0.0013) | (0.0005) | (0.0004) | (0.0000) | (0.0012) | (0.0010) | (0.0004) | (0.0008) | (0.0015) | (0.0008) | (0.0003) |
\({\mu }_{F}\) | − 0.001692 | 0.003022 | − 0.001683 | − 0.001395 | − 0.002882 | 0.003913 | − 0.002120 | − 0.002537 | − 0.005926 | 0.002633 | − 0.003001 | − 0.002559 | − 0.007078 | 0.003409 | − 0.006399 | − 0.006178 |
 | (0.0005) | (0.0011) | (0.0009) | (0.0009) | (0.0006) | (0.0012) | (0.0010) | (0.0009) | (0.0009) | (0.0014) | (0.0011) | (0.0010) | (0.0010) | (0.0015) | (0.0011) | (0.0010) |
\({\mu }_{X}\) | 0.008704 | 0.081062 | 0.036673 | 0.035420 | 0.009652 | 0.074079 | 0.037610 | 0.034647 | 0.008114 | 0.053493 | 0.032838 | 0.036395 | 0.014268 | 0.046245 | 0.016597 | 0.016590 |
 | (0.0015) | (0.0065) | (0.0039) | (0.0036) | (0.0016) | (0.0072) | (0.0050) | (0.0048) | (0.0010) | (0.0063) | (0.0055) | (0.0050) | (0.0018) | (0.0081) | (0.0055) | (0.0051) |
\({\sigma }_{D}\) | 0.001164 | 0.039900 | 0.015375 | 0.004566 | 0.000317 | 0.047942 | 0.015131 | 0.003470 | 0.000461 | 0.060355 | 0.016918 | 0.002468 | 0.040012 | 0.054911 | 0.011378 | 0.001465 |
 | (0.0010) | (0.0057) | (0.0031) | (0.0016) | (0.0002) | (0.0068) | (0.0031) | (0.0014) | (0.0002) | (0.0072) | (0.0042) | (0.0015) | (0.0078) | (0.0074) | (0.0034) | (0.0008) |
\({\sigma }_{F}\) | 0.001397 | 0.009865 | 0.002928 | 0.002541 | 0.000722 | 0.015150 | 0.002637 | 0.000405 | 0.001467 | 0.014908 | 0.003232 | 0.000142 | 0.021055 | 0.017009 | 0.001202 | 0.000231 |
 | (0.0011) | (0.0037) | (0.0016) | (0.0015) | (0.0002) | (0.0040) | (0.0017) | (0.0003) | (0.0002) | (0.0043) | (0.0019) | (0.0000) | (0.0037) | (0.0045) | (0.0006) | (0.0000) |
\({\sigma }_{X}\) | 0.006481 | 0.251397 | 0.147092 | 0.132927 | 0.005605 | 0.249127 | 0.089347 | 0.074064 | 0.006120 | 0.204447 | 0.080414 | 0.059903 | 0.045350 | 0.163749 | 0.061711 | 0.048265 |
 | (0.0005) | (0.0125) | (0.0092) | (0.0085) | (0.0001) | (0.0138) | (0.0067) | (0.0055) | (0.0002) | (0.0140) | (0.0069) | (0.0049) | (0.0077) | (0.0118) | (0.0054) | (0.0038) |
\({\rho }_{DF}\) | 0.117911 | − 0.120885 | 0.168473 | 0.129840 | 0.057794 | − 0.114276 | 0.052936 | 0.052605 | 0.036240 | 0.024893 | 0.063506 | 0.105965 | 0.044221 | 0.129292 | 0.179325 | 0.197009 |
 | (0.0201) | (0.0452) | (0.0393) | (0.0403) | (0.0211) | (0.0416) | (0.0335) | (0.0326) | (0.0233) | (0.0405) | (0.0312) | (0.0300) | (0.0225) | (0.0378) | (0.0314) | (0.0289) |
\({\rho }_{DX}\) | − 0.044294 | 0.239232 | 0.347351 | 0.338430 | − 0.106519 | 0.217913 | 0.222447 | 0.209593 | − 0.127541 | 0.202069 | 0.267598 | 0.244220 | − 0.265086 | 0.233772 | 0.208486 | 0.189261 |
 | (0.0181) | (0.0280) | (0.0237) | (0.0237) | (0.0197) | (0.0309) | (0.0285) | (0.0281) | (0.0198) | (0.0296) | (0.0280) | (0.0265) | (0.0251) | (0.0276) | (0.0283) | (0.0272) |
\({\rho }_{FX}\) | 0.036204 | − 0.196205 | − 0.348180 | − 0.351234 | − 0.018109 | − 0.175236 | − 0.250914 | − 0.228900 | 0.019705 | − 0.086937 | − 0.270286 | − 0.228922 | 0.111136 | − 0.081577 | − 0.208031 | − 0.203972 |
 | (0.0171) | (0.0293) | (0.0244) | (0.0237) | (0.0224) | (0.0286) | (0.0286) | (0.0278) | (0.0267) | (0.0296) | (0.0293) | (0.0281) | (0.0290) | (0.0289) | (0.0291) | (0.0278) |
\({h}_{1,D}\) | 0.058792 | − 0.129914 | − 0.093029 | − 0.079904 | 0.031523 | − 0.106096 | − 0.041526 | − 0.033477 | 0.032963 | − 0.085967 | − 0.039834 | − 0.030325 | 0.066753 | − 0.069152 | − 0.041629 | − 0.034419 |
 | (0.0052) | (0.0107) | (0.0120) | (0.0120) | (0.0107) | (0.0117) | (0.0129) | (0.0132) | (0.0122) | (0.0119) | (0.0142) | (0.0145) | (0.0132) | (0.0117) | (0.0126) | (0.0128) |
\({h}_{1,F}\) | 0.014723 | − 0.124973 | − 0.042283 | − 0.039590 | 0.000310 | − 0.074357 | − 0.017283 | − 0.005943 | − 0.021301 | − 0.048779 | 0.015095 | 0.021575 | − 0.048193 | − 0.002592 | 0.022504 | 0.026745 |
 | (0.0064) | (0.0121) | (0.0127) | (0.0128) | (0.0112) | (0.0125) | (0.0124) | (0.0123) | (0.0114) | (0.0133) | (0.0138) | (0.0141) | (0.0146) | (0.0131) | (0.0131) | (0.0134) |
\({h}_{1,X}\) | 0.025533 | 0.004156 | 0.004580 | 0.004003 | 0.037424 | 0.001015 | 0.017462 | 0.011677 | 0.044192 | 0.004052 | 0.005683 | 0.006648 | 0.071481 | 0.012248 | − 0.014873 | − 0.017806 |
 | (0.0054) | (0.0114) | (0.0109) | (0.0108) | (0.0047) | (0.0123) | (0.0119) | (0.0121) | (0.0062) | (0.0135) | (0.0130) | (0.0126) | (0.0111) | (0.0135) | (0.0133) | (0.0132) |
Panel (b): Jump Part | ||||||||||||||||
\({\theta }_{D,u}\left({\theta }_{D}\right)\) |  | − 0.103941 | − 0.078482 | − 0.035271 |  | − 0.127322 | − 0.063849 | − 0.036474 |  | − 0.117015 | − 0.105996 | − 0.034718 |  | − 0.105821 | − 0.087733 | − 0.032088 |
 |  | (0.0116) | (0.0077) | (0.0055) |  | (0.0129) | (0.0092) | (0.0062) |  | (0.0141) | (0.0097) | (0.0069) |  | (0.0116) | (0.0082) | (0.0060) |
\({\theta }_{F,u}\left({\theta }_{F}\right)\) |  | − 0.063852 | − 0.079472 | − 0.040376 |  | − 0.074380 | − 0.094229 | − 0.043811 |  | − 0.081537 | − 0.085240 | − 0.044208 |  | − 0.073420 | − 0.106547 | − 0.032464 |
 |  | (0.0113) | (0.0080) | (0.0061) |  | (0.0092) | (0.0090) | (0.0073) |  | (0.0104) | (0.0069) | (0.0066) |  | (0.0082) | (0.0103) | (0.0072) |
\({\theta }_{X,u}\left({\theta }_{X}\right)\) |  | 0.025426 | − 0.020360 | 0.062743 |  | − 0.008211 | − 0.010144 | 0.078574 |  | − 0.025338 | − 0.016671 | 0.094697 |  | − 0.012192 | − 0.079394 | 0.061559 |
 |  | (0.0168) | (0.0143) | (0.0087) |  | (0.0185) | (0.0158) | (0.0100) |  | (0.0179) | (0.0194) | (0.0132) |  | (0.0207) | (0.0199) | (0.0101) |
\({\theta }_{T,u}\left({\theta }_{T}\right)\) |  | − 0.129356 | − 0.049246 | − 0.019262 |  | − 0.095806 | − 0.026469 | − 0.010297 |  | − 0.078990 | − 0.019028 | − 0.011279 |  | − 0.069946 | − 0.010386 | − 0.006005 |
 |  | (0.0083) | (0.0056) | (0.0028) |  | (0.0064) | (0.0029) | (0.0014) |  | (0.0053) | (0.0022) | (0.0017) |  | (0.0049) | (0.0016) | (0.0013) |
\({\theta }_{D,d}\) |  |  |  | − 0.045663 |  |  |  | − 0.041517 |  |  |  | − 0.045810 |  |  |  | − 0.057510 |
 |  |  |  | (0.0065) |  |  |  | (0.0067) |  |  |  | (0.0089) |  |  |  | (0.0080) |
\({\theta }_{F,d}\) |  |  |  | − 0.033269 |  |  |  | − 0.043087 |  |  |  | − 0.043641 |  |  |  | − 0.071454 |
 |  |  |  | (0.0069) |  |  |  | (0.0078) |  |  |  | (0.0067) |  |  |  | (0.0103) |
\({\theta }_{X,d}\) |  |  |  | − 0.085976 |  |  |  | − 0.097170 |  |  |  | − 0.099785 |  |  |  | − 0.142869 |
 |  |  |  | (0.0099) |  |  |  | (0.0117) |  |  |  | (0.0106) |  |  |  | (0.0145) |
\({\theta }_{T,d}\) |  |  |  | − 0.032791 |  |  |  | − 0.020401 |  |  |  | − 0.015589 |  |  |  | − 0.007249 |
 |  |  |  | (0.0054) |  |  |  | (0.0026) |  |  |  | (0.0018) |  |  |  | (0.0011) |
\({\nu }_{D,u}\left({\nu }_{D}\right)\) | Â | 0.349882 | 0.303397 | 0.170164 | Â | 0.386543 | 0.291435 | 0.179542 | Â | 0.363802 | 0.358900 | 0.194860 | Â | 0.340497 | 0.328360 | 0.158263 |
 |  | (0.0200) | (0.0154) | (0.0156) |  | (0.0211) | (0.0153) | (0.0161) |  | (0.0230) | (0.0165) | (0.0160) |  | (0.0208) | (0.0169) | (0.0161) |
\({\nu }_{F,u}\left({\nu }_{F}\right)\) | Â | 0.296938 | 0.287969 | 0.181850 | Â | 0.295188 | 0.308004 | 0.189774 | Â | 0.305827 | 0.298842 | 0.185792 | Â | 0.274907 | 0.323946 | 0.150969 |
 |  | (0.0195) | (0.0141) | (0.0146) |  | (0.0175) | (0.0143) | (0.0156) |  | (0.0197) | (0.0138) | (0.0143) |  | (0.0171) | (0.0141) | (0.0142) |
\({\nu }_{X,u}\left({\nu }_{X}\right)\) | Â | 0.374565 | 0.310624 | 0.165345 | Â | 0.368033 | 0.353823 | 0.194037 | Â | 0.371654 | 0.340854 | 0.213995 | Â | 0.348479 | 0.330604 | 0.150092 |
 |  | (0.0159) | (0.0126) | (0.0131) |  | (0.0146) | (0.0131) | (0.0149) |  | (0.0139) | (0.0135) | (0.0154) |  | (0.0159) | (0.0132) | (0.0143) |
\({\nu }_{T,u}\) | Â | 0.391352 | 0.222043 | 0.107949 | Â | 0.364365 | 0.175146 | 0.081825 | Â | 0.338708 | 0.155643 | 0.080438 | Â | 0.324222 | 0.122733 | 0.055311 |
 |  | (0.0112) | (0.0097) | (0.0094) |  | (0.0107) | (0.0085) | (0.0071) |  | (0.0107) | (0.0082) | (0.0075) |  | (0.0104) | (0.0072) | (0.0063) |
\({\nu }_{D,d}\) | Â | Â | Â | 0.195819 | Â | Â | Â | 0.190442 | Â | Â | Â | 0.226936 | Â | Â | Â | 0.240378 |
 |  |  |  | (0.0169) |  |  |  | (0.0168) |  |  |  | (0.0178) |  |  |  | (0.0189) |
\({\nu }_{F,d}\) | Â | Â | Â | 0.153181 | Â | Â | Â | 0.176707 | Â | Â | Â | 0.184648 | Â | Â | Â | 0.224546 |
 |  |  |  | (0.0142) |  |  |  | (0.0151) |  |  |  | (0.0143) |  |  |  | (0.0165) |
\({\nu }_{X,d}\) | Â | Â | Â | 0.183590 | Â | Â | Â | 0.204909 | Â | Â | Â | 0.221071 | Â | Â | Â | 0.225019 |
 |  |  |  | (0.0147) |  |  |  | (0.0161) |  |  |  | (0.0159) |  |  |  | (0.0155) |
\({\nu }_{T,d}\) | Â | Â | Â | 0.134098 | Â | Â | Â | 0.116588 | Â | Â | Â | 0.109734 | Â | Â | Â | 0.084406 |
 |  |  |  | (0.0110) |  |  |  | (0.0095) |  |  |  | (0.0087) |  |  |  | (0.0068) |
\({\phi }_{DF,u}\left({\phi }_{DF}\right)\) |  |  | 0.091636 | 0.017486 |  |  | − 0.004755 | 0.023974 |  |  | 0.040313 | 0.022774 |  |  | 0.052980 | 0.024230 |
 |  |  | (0.0352) | (0.0268) |  |  | (0.0380) | (0.0298) |  |  | (0.0403) | (0.0313) |  |  | (0.0393) | (0.0268) |
\({\phi }_{DX,u}\left({\phi }_{DX}\right)\) |  |  | − 0.030493 | − 0.060249 |  |  | − 0.000962 | − 0.030938 |  |  | 0.021785 | − 0.020295 |  |  | 0.017621 | 0.003663 |
 |  |  | (0.0322) | (0.0216) |  |  | (0.0340) | (0.0258) |  |  | (0.0347) | (0.0272) |  |  | (0.0350) | (0.0236) |
\({\phi }_{FX,u}\left({\phi }_{FX}\right)\) |  |  | − 0.007026 | − 0.018610 |  |  | − 0.064709 | − 0.063282 |  |  | − 0.068927 | − 0.072276 |  |  | 0.029509 | − 0.040974 |
 |  |  | (0.0307) | (0.0232) |  |  | (0.0338) | (0.0263) |  |  | (0.0361) | (0.0272) |  |  | (0.0340) | (0.0231) |
\({\phi }_{DF,d}\) | Â | Â | Â | 0.018147 | Â | Â | Â | 0.014756 | Â | Â | Â | 0.013551 | Â | Â | Â | 0.041549 |
 |  |  |  | (0.0257) |  |  |  | (0.0286) |  |  |  | (0.0318) |  |  |  | (0.0314) |
\({\phi }_{DX,d}\) |  |  |  | 0.026804 |  |  |  | − 0.010328 |  |  |  | 0.009262 |  |  |  | 0.010109 |
 |  |  |  | (0.0233) |  |  |  | (0.0252) |  |  |  | (0.0266) |  |  |  | (0.0296) |
\({\phi }_{FX,d}\) |  |  |  | 0.059836 |  |  |  | − 0.010387 |  |  |  | 0.001933 |  |  |  | 0.109213 |
 |  |  |  | (0.0229) |  |  |  | (0.0249) |  |  |  | (0.0277) |  |  |  | (0.0264) |
\({\lambda }_{u}\left(\lambda \right)\) | Â | 0.273904 | 0.217572 | 0.094420 | Â | 0.296214 | 0.222632 | 0.100983 | Â | 0.307797 | 0.257508 | 0.098539 | Â | 0.344920 | 0.273139 | 0.089324 |
 |  | (0.0085) | (0.0065) | (0.0069) |  | (0.0099) | (0.0074) | (0.0073) |  | (0.0096) | (0.0095) | (0.0072) |  | (0.0127) | (0.0092) | (0.0084) |
\({\lambda }_{d}\) | Â | Â | Â | 0.120259 | Â | Â | Â | 0.120065 | Â | Â | Â | 0.140570 | Â | Â | Â | 0.176357 |
 |  |  |  | (0.0094) |  |  |  | (0.0098) |  |  |  | (0.0117) |  |  |  | (0.0121) |
\({h}_{D,u}\left({h}_{D}\right)\) |  | − 0.016247 | − 0.048444 | − 0.033923 |  | − 0.024678 | − 0.045467 | − 0.023176 |  | − 0.002077 | − 0.050795 | − 0.027759 |  | − 0.004745 | − 0.037503 | − 0.015255 |
 |  | (0.0090) | (0.0072) | (0.0060) |  | (0.0089) | (0.0070) | (0.0052) |  | (0.0084) | (0.0089) | (0.0079) |  | (0.0086) | (0.0086) | (0.0065) |
\({h}_{F,u}\left({h}_{F}\right)\) |  | 0.019391 | 0.016288 | 0.012627 |  | 0.012761 | 0.026561 | 0.028398 |  | − 0.018653 | − 0.009754 | 0.009051 |  | − 0.018498 | − 0.049899 | − 0.006722 |
 |  | (0.0117) | (0.0108) | (0.0082) |  | (0.0108) | (0.0119) | (0.0103) |  | (0.0105) | (0.0114) | (0.0087) |  | (0.0104) | (0.0114) | (0.0084) |
\({h}_{X,u}\left({h}_{X}\right)\) |  | 0.005524 | − 0.011550 | − 0.013180 |  | 0.009795 | 0.011827 | 0.009233 |  | 0.021382 | 0.048543 | 0.035173 |  | 0.013918 | 0.016387 | 0.011592 |
 |  | (0.0021) | (0.0042) | (0.0034) |  | (0.0023) | (0.0066) | (0.0055) |  | (0.0037) | (0.0090) | (0.0066) |  | (0.0033) | (0.0090) | (0.0063) |
\({h}_{D,d}\) |  |  |  | − 0.020069 |  |  |  | − 0.009306 |  |  |  | 0.003550 |  |  |  | − 0.020309 |
 |  |  |  | (0.0058) |  |  |  | (0.0067) |  |  |  | (0.0076) |  |  |  | (0.0065) |
\({h}_{F,d}\) |  |  |  | 0.004452 |  |  |  | − 0.009602 |  |  |  | − 0.019633 |  |  |  | − 0.031435 |
 |  |  |  | (0.0081) |  |  |  | (0.0094) |  |  |  | (0.0093) |  |  |  | (0.0093) |
\({h}_{X,d}\) | Â | Â | Â | 0.001473 | Â | Â | Â | 0.007825 | Â | Â | Â | 0.030325 | Â | Â | Â | 0.015973 |
 |  |  |  | (0.0030) |  |  |  | (0.0049) |  |  |  | (0.0064) |  |  |  | (0.0067) |
Panel (c): Log-Likelihood | ||||||||||||||||
LL | 2670.12 | 2800.71 | 3121.44 | 3172.58 | 2576.88 | 2627.62 | 3041.28 | 3122.81 | 2251.78 | 2387.07 | 2795.53 | 2882.96 | 1950.40 | 2225.34 | 2607.67 | 2670.89 |
LRT | Â | 261.18 | 641.46 | 102.29 | Â | 101.49 | 827.30 | 163.07 | Â | 270.58 | 816.91 | 174.86 | Â | 549.88 | 764.65 | 126.45 |