arXiv subjects

Liexin Cheng

Publications and source records attributed to Liexin Cheng.

5 recordsLinked to original sources

arXiv2026

RIDGE: An Autonomous Framework for Validation and Method Discovery in LLM-Generated Option Pricing

Automated code generation is becoming an important tool in quantitative finance, where large language models can generate option pricing implementations directly from mathematical model specifications. Validating such implementations, however, requires considerably more than conventional software testing: numerical pricing methods must remain mathematically consistent, numerically stable, and reliable across a wide range of model parameters. We introduce RIDGE, an autonomous validation framework in which generated pricing implementations are subjected to structured no-arbitrage tests, stress tests, benchmark comparisons, and consistency checks. Validation evidence is interpreted diagnostically, while the resulting knowledge is accumulated in a repository and reused across models and successive validation iterations. This enables systematic refinement of both the pricing implementation and the validation methodology. The framework is applied to five stochastic volatility models. Across these studies, all detected implementation defects are removed and, in two cases, the validation process reveals methodological limitations and motivates the development of alternative numerical methods. The supplementary material is available in the GitHub repository: https://github.com/ShQiangLiu/ridge.

q-fin.CP↗

arXiv2025

Fast Learning in Quantitative Finance with Extreme Learning Machine

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously addressed using deep neural networks, can be efficiently solved using single-layer neural networks without iterative gradient-based training. This is achieved through the extreme learning machine (ELM) framework. ELM utilizes a single-layer network with randomly initialized hidden nodes and output weights obtained via convex optimization, enabling rapid training and inference. We present various applications in both supervised and unsupervised learning settings, including option pricing, intraday return prediction, volatility surface fitting, and numerical solution of partial differential equations. Across these examples, ELM demonstrates notable improvements in computational efficiency while maintaining comparable accuracy and generalization compared to deep neural networks and classical machine learning methods. We also briefly discuss theoretical aspects of ELM implementation and its generalization capabilities.

q-fin.CP↗

arXiv2024

Joint Pricing in SPX and VIX Derivative Markets with Composite Change of Time Models

The Chicago Board Options Exchange Volatility Index (VIX) is calculated from SPX options and derivatives of VIX are also traded in market, which leads to the so-called ``consistent modeling" problem. This paper proposes a time-changed L\'evy model for log price with a composite change of time structure to capture both features of the implied SPX volatility and the implied volatility of volatility. Consistent modeling is achieved naturally via flexible choices of jumps and leverage effects, as well as the composition of time changes. Many celebrated models are covered as special cases. From this model, we derive an explicit form of the characteristic function for the asset price (SPX) and the pricing formula for European options as well as VIX options. The empirical results indicate great competence of the proposed model in the problem of joint calibration of the SPX/VIX Markets.

q-fin.MF↗

arXiv2024

Understanding Short-Term Implied Volatility Dynamics: A Model-Independent Approach Beyond Stochastic Volatility

This paper examines the short-term asymptotic behavior of the implied volatility surface, focusing on the at-the-money (ATM) skew and curvature. Rather than committing to a specific stochastic differential equation, we adopt a distribution-based approach by imposing cumulant conditions on the log-return distribution. Under these weak assumptions, we derive a quadratic expansion of implied volatility as a function of moneyness for near-the-money options and asymptotic expressions for ATM skew and curvature as time to maturity approaches zero, treating the decay rates of the third and fourth cumulants as independent parameters and introducing a marginal-type classifier. These results highlight differences in ATM asymptotic properties across different types of log return distributions and yield a unified, model-independent characterization of short-term smile dynamics in terms of the scaling laws of the marginal cumulants, covering regular/rough stochastic volatility and distribution-based ones like scalable gamma/CGMY martingale models alike from simple moment information. We subsequently present a distribution-based calibration method that not only effectively validates the analytical approximations, but also exhibits strong interpretability and consistent performance, and discuss potential connections to model-independent path-dependent applications via martingale optimal transport. Overall, our findings provide model-independent analytical tools for evaluating model performance against market stylized features, accurately approximating short-term option prices, and performing robust calibration.

q-fin.PR↗

arXiv2021

CatBoost model with synthetic features in application to loan risk assessment of small businesses

Loan risk for small businesses has long been a complex problem worthy of exploring. Predicting the loan risk can benefit entrepreneurship by developing more jobs for the society. CatBoost (Categorical Boosting) is a powerful machine learning algorithm suitable for dataset with many categorical variables like the dataset for forecasting loan risk. In this paper, we identify the important risk factors that contribute to loan status classification problem. Then we compare the performance between boosting-type algorithms(especially CatBoost) with other traditional yet popular ones. The dataset we adopt in the research comes from the U.S. Small Business Administration (SBA) and holds a very large sample size (899,164 observations and 27 features). In order to make the best use of the important features in the dataset, we propose a technique named "synthetic generation" to develop more combined features based on arithmetic operation, which ends up improving the accuracy and AUC of the original CatBoost model. We obtain a high accuracy of 95.84% and well-performed AUC of 98.80% compared with the existent literature of related research.

cs.CE↗