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

Financial Innovation

Table 3 Reproducibility of statistical properties with different generators

Model	\(\sigma\)	LU	FTD	VC	LE	CFVC		GLA
Model	\(\sigma\)	I(k)	\(\alpha\)	\(\beta\)	L(k)	\(\rho _{cf}^{\tau }(k)\)	\(\Delta \rho _{cf}^{\tau }(k)\)	\(T_\text {wait}^t(\theta =0.1)\)	\(T_\text {wait}^t(\theta =-0.1)\)
Sun Paper	0.0293	[−0.0581, 0.0603]	3.4924	1.1194	[−3.7770, 3.5193]	[0.0949, 0.6391]	[−0.0883, 0.0321]	6	7
BS	1.4418	[−0.3411, 0.9979]	23.6205	1.3601	[0.1566, 0.2481]	[0.8256, 1.0000 ]	[0.0000, 0.0000]	0	0
CEV	0.9011	[−0.2036, 0.9988]	5.5313	1.3448	[0.1150, 0.1298]	[0.9037, 1.0000 ]	[0.0000, 0.0000]	0	0
GARCH	0.0005	[−0.0582, 0.0604]	3.4920	1.0852	[−72.3026, 51.9073]	[−0.0376, 0.7069]	[−0.0897, 0.0230]	0	25
FinGAN-MLP	0.0347	[−0.0711, 0.0656]	5.4085	1.0844	[−3.7114, 5.0010]	[−0.0714, 0.6410 ]	[−0.0652, 0.0843]	6	10
FinGAN-LSTP	0.0312	[−0.0647, 0.0620]	6.4557	1.0835	[−3.1369, 3.1684]	[−0.0777, 0.6003 ]	[−0.0821, 0.0825 ]	3	3
FinGAN	0.0288	[−0.0627, 0.0593]	4.8038	1.1061	[−2.7933, 4.3075]	[−0.0265, 0.5292 ]	[−0.0865, 0.0567]	6	7

Table 3 reports the statistical properties for the daily stock returns of the Sun Paper and different stock return generators. LU stands for linear unpredictability, I(k) denotes the interval of the diminishing auto-correlation defined in Eq. 36. FTD stands for fat-tailed distribution, \(\alpha\) is the exponent of the power-law decay defined in Eq. 37. VC stands for volatility clustering, \(\beta\) is the exponent of the power-law decay of the auto-correlation function defined in Eq. 38. LE stands for leverage effect, L(k) is the range of lead-lag correlation function defined in Eq. 39. CFVC stands for coarse-fine volatility correlation, \(\rho _{cf}^{\tau }(k)\) is defined in Eq. 41, and \(\Delta \rho _{cf}^{\tau }(k)\) is defined in Eq. 40. GLA stands for gain/loss asymmetry, \(T_\text {wait}^t(\theta )\) is defined in Eq. 42. The sample period is from November 16, 2006 through June 30, 2021 and includes 3,556 observations