To achieve interoperability between unconnected ledgers, hash time lock contracts (HTLCs) are commonly used for cross-chain asset exchange. The solution tolerates transaction failure, and can “make the best out of worst” by allowing transacting agents to at least keep their original assets in case of an abort. Nonetheless, as an undesired outcome, reoccurring transaction failures prompt a critical and analytical examination of the protocol. In this study, we propose a game-theoretic framework to study the strategic behaviors of agents taking part in cross-chain atomic swaps implemented with HTLCs. We study the success rate of the transaction as a function of the exchange rate of the swap, the token price and its volatility, among other variables. We demonstrate that in an attempt to maximize one's own utility as asset price changes, either agent might withdraw from the swap. An extension of our model confirms that collateral deposits can improve the transaction success rate, motivating further research towards collateralization without a trusted third party. A second model variation suggests that a swap is more likely to succeed when agents dynamically adjust the exchange rate in response to price fluctuations.

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft constraints. Furthermore, our method can be combined with standard IVS models in quantitative finance, thus providing a NN-based correction when such models fail at replicating observed market prices. This lets practitioners use our approach as a plug-in on top of classical methods. Empirical results show that this approach is particularly useful when only sparse or erroneous data are available. We also quantify the uncertainty of the model predictions in regions with few or no observations. We further explore how deeper NNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard IVS models. By evaluating our method on both training sets, and testing sets, namely, we highlight both their capacity to reproduce observed prices and predict new ones.

We introduce the vine copula autoencoder (VCAE), a flexible generative model for high-dimensional distributions built in a straightforward three-step procedure. First, an autoencoder (AE) compresses the data into a lower dimensional representation. Second, the multivariate distribution of the encoded data is estimated with vine copulas. Third, a generative model is obtained by combining the estimated distribution with the decoder part of the AE. As such, the proposed approach can transform any already trained AE into a flexible generative model at a low computational cost. This is an advantage over existing generative models such as adversarial networks and variational AEs which can be difficult to train and can impose strong assumptions on the latent space. Experiments on MNIST, Street View House Numbers and Large-Scale CelebFaces Attributes datasets show that VCAEs can achieve competitive results to standard baselines.