Quantitative Finance

Richman, Ronald; Scognamiglio, Salvatore; Wüthrich, Mario V.

doi: 10.48550/arxiv.2409.16653pmid: N/A

Abstract:Inspired by the large success of Transformers in Large Language Models, these architectures are increasingly applied to tabular data. This is achieved by embedding tabular data into low-dimensional Euclidean spaces resulting in similar structures as time-series data. We introduce a novel credibility mechanism to this Transformer architecture. This credibility mechanism is based on a special token that should be seen as an encoder that consists of a credibility weighted average of prior information and observation based information. We demonstrate that this novel credibility mechanism is very beneficial to stabilize training, and our Credibility Transformer leads to predictive models that are superior to state-of-the-art deep learning models.

Zhang, Yan; Tian, Yixiang; Chen, Lin; Wang, Qi

doi: 10.48550/arxiv.2409.12831pmid: N/A

Abstract:The implicit government guarantee hampers the recognition and management of risks by all stakeholders in the bond market, and it has led to excessive debt for local governments or state-owned enterprises. To prevent the risk of local government debt defaults and reduce investors' expectations of implicit government guarantees, various regulatory departments have issued a series of policy documents related to municipal investment bonds. By employing text mining techniques on policy documents related to municipal investment bond, and utilizing the PMC index model to assess the effectiveness of policy documents. This paper proposes a novel method for quantifying the intensity of implicit governmental guarantees based on PMC index model. The intensity of implicit governmental guarantees is inversely correlated with the PMC index of policies aimed at de-implicitizing governmental guarantees. Then as these policies become more effective, the intensity of implicit governmental guarantees diminishes correspondingly. These findings indicate that recent policies related to municipal investment bond have indeed succeeded in reducing implicit governmental guarantee intensity, and these policies have achieved the goal of risk management. Furthermore, it was showed that the intensity of implicit governmental guarantee affected by diverse aspects of these policies such as effectiveness, clarity, and specificity, as well as incentive and assurance mechanisms.

Attal, Elie; Allez, Romain

doi: 10.48550/arxiv.2409.17086pmid: N/A

Abstract:We consider the eigenvectors of the principal minor of dimension $n< N$ of the Dyson Brownian motion in $\mathbb{R}^{N}$ and investigate their asymptotic overlaps with the eigenvectors of the full matrix in the limit of large dimension. We explicitly compute the limiting rescaled mean squared overlaps in the large $n\,, N$ limit with $n\,/\,N$ tending to a fixed ratio $q\,$, for any initial symmetric matrix $A\,$. This is accomplished using a Burgers-type evolution equation for a specific resolvent. In the GOE case, our formula simplifies, and we identify an eigenvector analogue of the well-known interlacing of eigenvalues. We investigate in particular the case where $A$ has isolated eigenvalues. Our method is based on analysing the eigenvector flow under the Dyson Brownian motion.

Wei, Jiaqin; Xia, Jianming; Zhao, Qian

doi: 10.48550/arxiv.2409.19259pmid: N/A

Abstract:We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available.

Jung, Jiwon; Lee, Kiseop

doi: 10.48550/arxiv.2409.02277pmid: N/A

Abstract:Managing high-frequency data in a limit order book (LOB) is a complex task that often exceeds the capabilities of conventional time-series forecasting models. Accurately predicting the entire multi-level LOB, beyond just the mid-price, is essential for understanding high-frequency market dynamics. However, this task is challenging due to the complex interdependencies among compound attributes within each dimension, such as order types, features, and levels. In this study, we explore advanced multidimensional sequence-to-sequence models to forecast the entire multi-level LOB, including order prices and volumes. Our main contribution is the development of a compound multivariate embedding method designed to capture the complex relationships between spatiotemporal features. Empirical results show that our method outperforms other multivariate forecasting methods, achieving the lowest forecasting error while preserving the ordinal structure of the LOB.

Yang, Jiefei;Li, Guanglian

doi: 10.48550/arxiv.2409.06937pmid: N/A

Abstract:We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which consists of subnetwork parameterization of a continuation value and spatial gradients from present up to the stopping time. Notable features of the method include: (i) The martingale part in the loss function reduces the variance of stochastic gradients, which facilitates the training of the neural networks as well as alleviates the error propagation of value function approximation; (ii) this martingale approximates the martingale in the Doob-Meyer decomposition, and thus leads to a true upper bound for the optimal value in a non-nested Monte Carlo way. We test the proposed method in American option pricing problems, where the spatial gradient network yields the hedging ratio directly.

Dohn, Simon; Hansen, Kristoffer Arnsfelt; Klinkby, Asger

doi: 10.48550/arxiv.2409.18717pmid: N/A

Abstract:We study computational problems in financial networks of banks connected by debt contracts and credit default swaps (CDSs). A main problem is to determine \emph{clearing} payments, for instance right after some banks have been exposed to a financial shock. Previous works have shown the $\varepsilon$-approximate version of the problem to be $\mathrm{PPAD}$-complete and the exact problem $\mathrm{FIXP}$-complete. We show that $\mathrm{PPAD}$-hardness hold when $\varepsilon \approx 0.101$, improving the previously best bound significantly. Due to the fact that the clearing problem typically does not have a unique solution, or that it may not have a solution at all in the presence of default costs, several natural decision problems are also of great interest. We show two such problems to be $\exists\mathbb{R}$-complete, complementing previous $\mathrm{NP}$-hardness results for the approximate setting.

Unnikrishnan, Ananya

doi: 10.48550/arxiv.2409.19706pmid: N/A

Abstract:An accurate valuation of American call options is critical in most financial decision making environments. However, traditional models like the Barone-Adesi Whaley (B-AW) and Binomial Option Pricing (BOP) methods fall short in handling the complexities of early exercise and market dynamics present in American options. This paper proposes a Modular Neural Network (MNN) model which aims to capture the key aspects of American options pricing. By dividing the prediction process into specialized modules, the MNN effectively models the non-linear interactions that drive American call options pricing. Experimental results indicate that the MNN model outperform both traditional models as well as a simpler Feed-forward Neural Network (FNN) across multiple stocks (AAPL, NVDA, QQQ), with significantly lower RMSE and nRMSE (by mean). These findings highlight the potential of MNNs as a powerful tool to improve the accuracy of predicting option prices.

Armstrong, John; Tatlow, George

doi: 10.48550/arxiv.2409.13567pmid: N/A

Abstract:We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black--Scholes model then we find the network will successfully learn the Black-Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black--Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs.

Elsts, Atis; Klas, Krešimir

doi: 10.48550/arxiv.2409.12803pmid: N/A

Abstract:Concentrated liquidity (CL) provisioning is a way how to improve the capital efficiency of Automated Market Makers (AMM). Allowing liquidity providers to use leverage is a step towards even higher capital efficiency. A number of Decentralized Finance (DeFi) protocols implement this technique in conjunction with overcollateralized lending. However, the properties of leveraged CL positions have not been formalized and are poorly understood in practice. This article describes the principles of a leveraged CL provisioning protocol, formally models the notions of margin level, assets, and debt, and proves that within this model, leveraged LP positions possess several properties that make them safe to use.