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Table 5 Pricing performance across different models: MAE

From: DeepPricing: pricing convertible bonds based on financial time-series generative adversarial networks

 

BS

CEV\((\beta =1)\)

GARCH(1,1)

FinGAN-MLP

FinGAN-LSTM

DeepPicing

Panel A. MAE

All

12.0287

11.8763

11.1084

10.8231

10.2431

9.8903

Equity-liked

16.188

15.0215

13.4516

11.4863

10.8942

10.1721

Balanced

9.6481

8.1742

7.6872

7.6196

7.3534

7.0184

Bond-liked

9.325

8.0184

7.4203

7.3255

7.1573

6.9218

Bull market

12.8915

11.7632

10.7654

10.1951

9.7792

9.1293

Direction-less market

6.6288

5.9824

5.7324

5.4552

5.2999

5.1932

Bear market

11.9657

10.9873

9.8935

8.8601

8.6137

8.1097

In-the-money

9.7683

8.2943

7.6729

7.4353

7.1933

6.8762

At-the-money

8.7610

7.4985

7.9832

6.9882

6.5759

6.3291

Out-of-the-money

15.4354

14.8621

14.9824

11.8153

11.4910

10.0295

Panel B. \(\Delta \text {MAE}_{i|\text {CEV}(\beta =1)}\)

All

1.27

0.00

−6.68

−9.29

−14.79

−18.3

Equity-liked

7.48

0.00

−11.04

−26.83

−32.13

−38.98

Balanced

16.58

0.00

−6.14

−7.03

−10.58

−15.24

Bond-liked

15.1

0.00

−7.75

−9.04

−11.36

−14.71

Bull market

9.16

0.00

−8.86

−14.31

−18.47

−25.35

Direction-less market

10.26

0.00

−4.27

−9.23

−12.11

−14.15

Bear market

8.53

0.00

−10.49

−21.52

−24.34

−30.37

In-the-money

16.36

0.00

−7.79

−10.93

−14.24

−18.75

At-the-money

15.56

0.00

6.26

−7.05

−13.13

−16.95

Out-of-the-money

3.79

0.00

0.81

−22.94

−25.73

−39.33

Panel C. \(\Delta \text {MAE}_{i|\text {GARCH}(1,1)}\)

All

7.96

6.68

0.00

−2.60

−8.11

−11.61

Equity-liked

18.52

11.04

0.00

−15.79

−21.09

−27.94

Balanced

22.72

6.14

0.00

−0.88

−4.44

−9.1

Bond-liked

22.85

7.75

0.00

−1.29

−3.61

−6.95

Bull market

18.02

8.86

0.00

−5.44

−9.61

−16.48

Direction-less market

14.53

4.27

0.00

−4.96

−7.84

−9.88

Bear market

19.02

10.49

0.00

−11.03

−13.85

−19.88

In-the-money

24.15

7.79

0.00

−3.15

−6.45

−10.96

At-the-money

9.3

−6.26

0.00

−13.31

−19.39

−23.22

Out-of-the-money

2.98

−0.81

0.00

−23.75

−26.53

−40.13

Panel D. \(\Delta \text {MAE}_{i|\text {FinGAN-MLP}}\)

All

10.56

9.29

2.60

0.00

−5.51

−9.01

Equity-liked

34.31

26.83

15.79

0.00

−5.29

−12.15

Balanced

23.60

7.03

0.88

0.00

−3.56

−8.22

Bond-liked

24.13

9.04

1.29

0.00

−2.32

−5.67

Bull market

23.47

14.31

5.44

0.00

−4.16

−11.04

Direction-less market

19.49

9.23

4.96

0.00

−2.89

−4.92

Bear market

30.05

21.52

11.03

0.00

−2.82

−8.85

In-the-money

27.29

10.93

3.15

0.00

−3.31

−7.82

At-the-money

22.61

7.05

13.31

0.00

−6.08

−9.91

Out-of-the-money

26.73

22.94

23.75

0.00

−2.78

−16.39

Panel E. \(\Delta \text {MAE}_{i|\text {FinGAN-LSTM}}\)

All

16.07

14.79

8.11

5.51

0.00

−3.50

Equity-liked

39.60

32.13

21.09

5.29

0.00

−6.86

Balanced

27.16

10.58

4.44

3.56

0.00

−4.66

Bond-liked

26.46

11.36

3.61

2.32

0.00

−3.35

Bull market

27.63

18.47

9.61

4.16

0.00

−6.88

Direction-less market

22.37

12.11

7.84

2.89

0.00

−2.03

Bear market

32.87

24.34

13.85

2.82

0.00

−6.03

In-the−money

30.60

14.24

6.45

3.31

0.00

−4.51

At-the-money

28.69

13.13

19.39

6.08

0.00

−3.83

Out-of-the-money

29.51

25.73

26.53

2.78

0.00

−13.60

Panel F. \(\Delta \text {MAE}_{i|\text {DeepPricing}}\)

All

19.57

18.3

11.61

9.01

3.50

0.00

Equity-liked

46.46

38.98

27.94

12.15

6.86

0.00

Balanced

31.82

15.24

9.1

8.21

4.66

0.00

Bond-liked

29.8

14.71

6.95

5.67

3.35

0.00

Bull market

34.51

25.35

16.48

11.04

6.88

0.00

Direction-less market

24.41

14.15

9.88

4.92

2.03

0.00

Bear market

38.9

30.37

19.88

8.85

6.03

0.00

In-the-money

35.11

18.75

10.96

7.82

4.51

0.00

At-the-money

32.52

16.95

23.22

9.91

3.83

0.00

Out-of-the-money

43.11

39.33

40.13

16.39

13.60

0.00

  1. Table 5 shows the MAE performance metrics across the different models for robustness test. The metric \(\text {MAE}_i\) stands for the percentage error of a model i as given by Eq. 45. The metric \(\Delta \text {MAE}_{i|j}\) measures the pricing performance difference of a model i relative to a model j, which is defined by Eq. 46. The debt-liked convertible bonds, the balanced convertible bonds and the equity-liked convertible bonds is determined by the sensitivity of the convertible bond value to its underlying common stock and defined as \(\Delta\) (Eq. 23) belongingness to the intervals [0, 0.33]; [0.33, 0.66]; and [0.66, 1], respectively. Market states is classified by bull market including subperiod from January 01, 2014 to June 12, 2015 and subperiod from January 01, 2019 to June 30, 2021, bear market including subperiod from January 01, 2010 to December 31, 2013; subperiod from June 15, 2015 to January 29, 2016; subperiod from January 01, 2018 to December 31, 2018 and direction-less market (including subperiod from February 01, 2016 to December 31, 2017. Moneyness is defined as the \(\xi =\text {S}_t/\text {K}_t\), where \(\text {K}_t\) is the conversion price and \(\text {S}_t\) is the close price of underlying stock. A convertible bond is said to be out-of-the-money if its \(\xi <0.99\); at the money if \(\xi \in [0.99,1.01]\); in-the-money if \(\xi > 1.01\). The sample period is from January 01, 2010 through June 30, 2021 and includes 125,306 observations