Skip to main content

Table 3 Parametric estimation results for GBP/USD

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)

\({\nu }_{D,u}\left({\nu }_{D}\right)\)

 

0.349882

0.303397

0.170164

 

0.386543

0.291435

0.179542

 

0.363802

0.358900

0.194860

 

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)

\({\nu }_{F,u}\left({\nu }_{F}\right)\)

 

0.296938

0.287969

0.181850

 

0.295188

0.308004

0.189774

 

0.305827

0.298842

0.185792

 

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)

\({\nu }_{X,u}\left({\nu }_{X}\right)\)

 

0.374565

0.310624

0.165345

 

0.368033

0.353823

0.194037

 

0.371654

0.340854

0.213995

 

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)

\({\nu }_{T,u}\)

 

0.391352

0.222043

0.107949

 

0.364365

0.175146

0.081825

 

0.338708

0.155643

0.080438

 

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)

\({\nu }_{D,d}\)

   

0.195819

   

0.190442

   

0.226936

   

0.240378

    

(0.0169)

   

(0.0168)

   

(0.0178)

   

(0.0189)

\({\nu }_{F,d}\)

   

0.153181

   

0.176707

   

0.184648

   

0.224546

    

(0.0142)

   

(0.0151)

   

(0.0143)

   

(0.0165)

\({\nu }_{X,d}\)

   

0.183590

   

0.204909

   

0.221071

   

0.225019

    

(0.0147)

   

(0.0161)

   

(0.0159)

   

(0.0155)

\({\nu }_{T,d}\)

   

0.134098

   

0.116588

   

0.109734

   

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)

\({\phi }_{DF,d}\)

   

0.018147

   

0.014756

   

0.013551

   

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)

\({\lambda }_{u}\left(\lambda \right)\)

 

0.273904

0.217572

0.094420

 

0.296214

0.222632

0.100983

 

0.307797

0.257508

0.098539

 

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)

\({\lambda }_{d}\)

   

0.120259

   

0.120065

   

0.140570

   

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)

\({h}_{X,d}\)

   

0.001473

   

0.007825

   

0.030325

   

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

 

261.18

641.46

102.29

 

101.49

827.30

163.07

 

270.58

816.91

174.86

 

549.88

764.65

126.45

  1. The results are calibrated from the sample shown in Table 1. This table lists the average and standard error of the mean of parametric estimation results for GBP/USD. The results are divided into the continuous part (Panel (a)) and the jump part (Panel (b)). For the jump part’s parameters in CB–ISJ and CB–CSJ models, the notations are shown in the brackets. For example, the mean of jump amplitude for domestic interest rate in CB–ISJ and CB–CSJ models is \({\uptheta }_{\mathrm{D}}\) in the bracket