Jaehyung Choi

Young Shin Kim, Hyangju Kim, Jaehyung Choi

This paper explores Artificial Neural Network (ANN) as a model-free solution for a calibration algorithm of option pricing models. We construct ANNs to calibrate parameters for two well-known GARCH-type option pricing models: Duan's GARCH and the classical tempered stable GARCH that significantly improve upon the limitation of the Black-Scholes model but have suffered from computation complexity. To mitigate this technical difficulty, we train ANNs with a dataset generated by Monte Carlo Simulation (MCS) method and apply them to calibrate optimal parameters. The performance results indicate that the ANN approach consistently outperforms MCS and takes advantage of faster computation times once trained. The Greeks of options are also discussed.

Jaehyung Choi

We develop the information geometry of Lévy processes. Deriving $α$-divergences directly in terms of the Lévy triplets of the Lévy processes, we identify Fisher information matrix and $α$-connection on the statistical manifold. In addition, we discuss statistical implications of this information geometry, including bias reduction estimation and Bayesian predictive priors. Several Lévy processes, broadly used for financial modeling such as tempered stable processes, the CGMY model, variance gamma processes, and the Merton model, are investigated through their differential-geometric structures as illustrative examples.

Jaekyum Kim, Junho Koh, Yecheol Kim et al.

The goal of multi-modal learning is to use complimentary information on the relevant task provided by the multiple modalities to achieve reliable and robust performance. Recently, deep learning has led significant improvement in multi-modal learning by allowing for the information fusion in the intermediate feature levels. This paper addresses a problem of designing robust deep multi-modal learning architecture in the presence of imperfect modalities. We introduce deep fusion architecture for object detection which processes each modality using the separate convolutional neural network (CNN) and constructs the joint feature map by combining the intermediate features from the CNNs. In order to facilitate the robustness to the degraded modalities, we employ the gated information fusion (GIF) network which weights the contribution from each modality according to the input feature maps to be fused. The weights are determined through the convolutional layers followed by a sigmoid function and trained along with the information fusion network in an end-to-end fashion. Our experiments show that the proposed GIF network offers the additional architectural flexibility to achieve robust performance in handling some degraded modalities, and show a significant performance improvement based on Single Shot Detector (SSD) for KITTI dataset using the proposed fusion network and data augmentation schemes.

Jaehyung Choi, Andrew P. Mullhaupt

We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The Hermitian structure of the Kähler manifold is explicitly emergent if and only if the impulse response function of the highest degree in $z$ is constant in model parameters. The Kählerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, $α$-generalization on the geometric tensors is linear in $α$. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on Kähler manifolds are in much simpler forms than those of the non-Kähler manifolds. Several time series models are studied in the Kählerian information geometry.