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Table 4 Pricing performance across different models: MAPE

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

 

BS

CEV\((\beta =1)\)

GARCH(1,1)

FinGAN-MLP

FinGAN-LSTM

DeepPricing

Panel A. MAPE

All

0.0934

0.0924

0.0893

0.0831

0.0797

0.0721

Equity-liked

0.1009

0.0983

0.0924

0.0874

0.0829

0.0774

Balanced

0.0908

0.0827

0.0783

0.0773

0.0746

0.0712

Bond-liked

0.0874

0.0832

0.0794

0.0785

0.0757

0.0722

Bull market

0.1302

0.1243

0.1138

0.1086

0.0993

0.0927

Direction-less market

0.0619

0.0612

0.0582

0.0562

0.0546

0.0535

Bear market

0.0879

0.0874

0.0821

0.0791

0.0769

0.0724

In-the-money

0.0932

0.0926

0.0914

0.0891

0.0862

0.0824

At-the-money

0.0731

0.0713

0.0704

0.0693

0.0681

0.0676

Out-of-the-money

0.0953

0.0914

0.0893

0.0867

0.0841

0.0804

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

All

1.07

0.00

−3.41

−10.61

−14.79

−24.81

Equity-liked

2.61

0.00

−6.19

−11.75

−17.04

−23.90

Balanced

9.31

0.00

−5.47

−6.75

−10.31

−14.97

Bond-liked

4.90

0.00

-4.67

-5.81

-9.47

-14.24

Bull market

4.64

0.00

−8.83

−13.50

−22.46

−29.33

Direction-less market

1.12

0.00

−5.03

−8.52

−11.41

−13.45

Bear market

0.52

0.00

−6.26

−9.98

−12.80

−18.83

In-the-money

0.64

0.00

−1.30

−3.85

−7.16

−11.67

At-the-money

2.48

0.00

−1.27

−2.85

−4.59

−5.33

Out-of-the-money

4.17

0.00

−2.32

−5.28

−8.32

−12.82

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

All

4.49

3.41

0.00

−7.20

−11.37

−21.39

Equity-liked

8.80

6.19

0.00

−5.56

−10.85

−17.71

Balanced

14.78

5.47

0.00

−1.29

−4.84

−9.51

Bond-liked

9.58

4.67

0.00

−1.14

−4.77

−9.56

Bull market

13.46

8.83

0.00

−4.68

−13.63

−20.51

Direction-less market

6.14

5.03

0.00

−3.50

−6.39

−8.42

Bear market

6.77

6.26

0.00

−3.72

−6.54

−12.57

In-the-money

1.95

1.30

0.00

−2.55

−5.86

−10.37

At-the-money

3.75

1.27

0.00

−1.57

−3.32

−4.06

Out-of-the-money

6.49

2.32

0.00

−2.95

−6.00

−10.50

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

All

11.68

10.61

7.20

0.00

−4.18

−14.20

Equity-liked

14.36

11.75

5.56

0.00

−5.29

−12.15

Balanced

16.10

6.75

1.29

0.00

−3.56

−8.22

Bond-liked

10.74

5.81

1.14

0.00

−3.63

−8.37

Bull market

18.14

13.50

4.68

0.00

−8.95

−15.83

Direction-less market

9.66

8.52

3.50

0.00

−2.89

−4.92

Bear market

10.55

9.98

3.72

0.00

−2.82

−8.85

In-the-money

4.50

3.85

2.55

0.00

−3.31

−7.82

At-the-money

5.34

2.85

1.57

0.00

−1.75

−2.48

Out-of-the-money

9.46

5.28

2.95

0.00

−3.04

−7.54

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

All

15.86

14.79

11.37

4.18

0.00

−10.02

Equity-liked

19.65

17.04

10.85

5.29

0.00

−6.86

Balanced

19.65

10.31

4.84

3.56

0.00

−4.66

Bond-liked

14.37

9.45

4.77

3.63

0.00

−4.73

Bull market

27.09

22.46

13.63

8.95

0.00

−6.88

Direction-less market

12.55

11.41

6.39

2.89

0.00

−2.04

Bear market

13.37

12.80

6.54

2.82

0.00

−6.03

In-the-money

7.81

7.16

5.86

3.31

0.00

−4.51

At-the-money

7.09

4.59

3.32

1.75

0.00

−0.74

Out-of-the-money

12.50

8.32

6.00

3.04

0.00

−4.50

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

All

25.88

24.81

21.39

14.20

10.02

0.00

Equity-liked

26.51

23.90

17.71

12.15

6.86

0.00

Balanced

24.28

14.97

9.51

8.22

4.66

0.00

Bond-liked

19.14

14.24

9.56

8.37

4.73

0.00

Bull market

33.97

29.33

20.51

15.83

6.88

0.00

Direction-less market

14.56

13.45

8.42

4.92

2.04

0.00

Bear market

19.35

18.83

12.57

8.85

6.03

0.00

In-the-money

12.31

11.67

10.37

7.82

4.51

0.00

At-the-money

7.81

5.33

4.06

2.48

0.74

0.00

Out-of-the-money

16.99

12.82

10.50

7.54

4.50

0.00

  1. Table 4 shows the MAPE performance metrics across the different models. The metric \(\text {MAPE}_i\) stands for the percentage error of a model i as given by Eq. 43. The metric \(\Delta \text {MAPE}_{i|j}\) measures the pricing performance difference of a model i relative to a model j, which is defined by Eq. 44. 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