Table 10 The Heston parameters are estimated with the CaNN by calibrating to a data set generated by the Bates model. ‘Ground total squared error’ refers to the sum of the differences between \(\sigma ^{*}_{\text{imp}}\) and \(\sigma _{\text{imp}}\), where \(\sigma _{\text{imp}}\) is obtained using the COS and Brent methods with already calibrated Heston parameter values. For a single calibration case, the computing time fluctuates slightly, as the CPU or GPU performance may be influenced by external factors. Function evaluations should be a reliable measure to estimate the time
From: A neural network-based framework for financial model calibration
– | Calibration | Rare jump | Common jump | Weighting ATM | |||
|---|---|---|---|---|---|---|---|
Parameters | Search space | Bates | Heston | Bates | Heston | Bates | Heston |
Intensity of jumps, \(\lambda _{J}\) | – | 0.1 | – | 1.0 | – | 1.0 | – |
Mean of jumps, \(\mu _{J}\) | – | 0.1 | – | 0.1 | – | 0.1 | – |
Variance of jumps, \(\nu ^{2}_{J}\) | – | \( 0.1^{2} \) | – | \( 0.1^{2} \) | – | \( 0.1^{2} \) | – |
Correlation, ρ | [−0.9,0.0] | −0.3 | −0.284 | −0.3 | −0.135 | −0.3 | −0.164 |
Reversion speed, κ | [0.1,3.0] | 1.0 | 1.140 | 1.0 | 1.050 | 1.0 | 1.205 |
Long variance, ν̄ | [0.01,0.5] | 0.1 | 0.100 | 0.1 | 0.120 | 0.1 | 0.114 |
Volatility of volatility, γ | [0.01,0.8] | 0.7 | 0.728 | 0.7 | 0.701 | 0.7 | 0.604 |
Initial variance, \(\nu _{0}\) | [0.01,0.5] | 0.1 | 0.103 | 0.1 | 0.119 | 0.1 | 0.115 |
Function evaluations | CaNN | – | 162,890 | – | 155,680 | – | 258,300 |
Time(seconds) | GPU | – | 0.45 | – | 0.40 | – | 0.7 |
Total Squared Error | Ground | – | 1.38 × 10−6 | – | 5.19 × 10−6 | – | 5.95 × 10−5 |