Risk valuation of quanto derivatives on temperature and electricity ArXiv ID: 2310.07692 “View on arXiv” Authors: Unknown Abstract This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian Lévy process, which allows to include dependence between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD). ...

Uses of Sub-sample Estimates to Reduce Errors in Stochastic Optimization Models ArXiv ID: 2310.07052 “View on arXiv” Authors: Unknown Abstract Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter’s distribution or with some form of sample. With large numbers of such parameters, optimization of the resulting model is often driven by mis-specifications or extreme sample characteristics, resulting in solutions that are far from a true optimum. This paper describes how asymptotic convergence results may not be useful in large-scale problems and how the optimization of problems based on sub-sample estimates may achieve improved results over models using full-sample solution estimates. A motivating example and numerical results from a portfolio optimization problem demonstrate the potential improvement. A theoretical analysis also provides insight into the structure of problems where sub-sample optimization may be most beneficial. ...

Anomalous diffusion and price impact in the fluid-limit of an order book ArXiv ID: 2310.06079 “View on arXiv” Authors: Unknown Abstract We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. This models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. We study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. Concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generate kinks in the price impact. We use cubic spline interpolation to generate smoothed price impact curves. The work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method. ...

Differential Quantile-Based Sensitivity in Discontinuous Models ArXiv ID: 2310.06151 “View on arXiv” Authors: Unknown Abstract Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a model parameter can reveal input-output relations and the relative importance of model parameters and input variables. Nonetheless, it is unclear how such derivatives should be taken when the model function has discontinuities and/or input variables are discrete. We present a general framework for addressing such problems, considering derivatives of quantile-based output risk measures, with respect to distortions to random input variables (risk factors), which impact the model output through step-functions. We prove that, subject to weak technical conditions, the derivatives are well-defined and derive the corresponding formulas. We apply our results to the sensitivity analysis of compound risk models and to a numerical study of reinsurance credit risk in a multi-line insurance portfolio. ...

Dual-Class Stocks: Can They Serve as Effective Predictors? ArXiv ID: 2310.16845 “View on arXiv” Authors: Unknown Abstract Kardemir Karabuk Iron Steel Industry Trade & Co. Inc., ranked as the 24th largest industrial company in Turkey, offers three distinct stocks listed on the Borsa Istanbul: KRDMA, KRDMB, and KRDMD. These stocks, sharing the sole difference in voting power, have exhibited significant price divergence over an extended period. This paper conducts an in-depth analysis of the divergence patterns observed in these three stock prices from January 2001 to July 2023. Additionally, it introduces an innovative training set selection rule tailored for LSTM models, incorporating a rolling training set, and demonstrates its significant predictive superiority over the conventional use of LSTM models with large training sets. Despite their strong correlation, the study found no compelling evidence supporting the efficiency of dual-class stocks as predictors of each other’s performance. ...

Integrating Stock Features and Global Information via Large Language Models for Enhanced Stock Return Prediction ArXiv ID: 2310.05627 “View on arXiv” Authors: Unknown Abstract The remarkable achievements and rapid advancements of Large Language Models (LLMs) such as ChatGPT and GPT-4 have showcased their immense potential in quantitative investment. Traders can effectively leverage these LLMs to analyze financial news and predict stock returns accurately. However, integrating LLMs into existing quantitative models presents two primary challenges: the insufficient utilization of semantic information embedded within LLMs and the difficulties in aligning the latent information within LLMs with pre-existing quantitative stock features. We propose a novel framework consisting of two components to surmount these challenges. The first component, the Local-Global (LG) model, introduces three distinct strategies for modeling global information. These approaches are grounded respectively on stock features, the capabilities of LLMs, and a hybrid method combining the two paradigms. The second component, Self-Correlated Reinforcement Learning (SCRL), focuses on aligning the embeddings of financial news generated by LLMs with stock features within the same semantic space. By implementing our framework, we have demonstrated superior performance in Rank Information Coefficient and returns, particularly compared to models relying only on stock features in the China A-share market. ...

An Information Theory Approach to the Stock and Cryptocurrency Market: A Statistical Equilibrium Perspective ArXiv ID: 2310.04907 “View on arXiv” Authors: Unknown Abstract We study the stochastic structure of cryptocurrency rates of returns as compared to stock returns by focusing on the associated cross-sectional distributions. We build two datasets. The first comprises forty-six major cryptocurrencies, and the second includes all the companies listed in the S&P 500. We collect individual data from January 2017 until December 2022. We then apply the Quantal Response Statistical Equilibrium (QRSE) model to recover the cross-sectional frequency distribution of the daily returns of cryptocurrencies and S&P 500 companies. We study the stochastic structure of these two markets and the properties of investors’ behavior over bear and bull trends. Finally, we compare the degree of informational efficiency of these two markets. ...

FinGPT: Instruction Tuning Benchmark for Open-Source Large Language Models in Financial Datasets ArXiv ID: 2310.04793 “View on arXiv” Authors: Unknown Abstract In the swiftly expanding domain of Natural Language Processing (NLP), the potential of GPT-based models for the financial sector is increasingly evident. However, the integration of these models with financial datasets presents challenges, notably in determining their adeptness and relevance. This paper introduces a distinctive approach anchored in the Instruction Tuning paradigm for open-source large language models, specifically adapted for financial contexts. Through this methodology, we capitalize on the interoperability of open-source models, ensuring a seamless and transparent integration. We begin by explaining the Instruction Tuning paradigm, highlighting its effectiveness for immediate integration. The paper presents a benchmarking scheme designed for end-to-end training and testing, employing a cost-effective progression. Firstly, we assess basic competencies and fundamental tasks, such as Named Entity Recognition (NER) and sentiment analysis to enhance specialization. Next, we delve into a comprehensive model, executing multi-task operations by amalgamating all instructional tunings to examine versatility. Finally, we explore the zero-shot capabilities by earmarking unseen tasks and incorporating novel datasets to understand adaptability in uncharted terrains. Such a paradigm fortifies the principles of openness and reproducibility, laying a robust foundation for future investigations in open-source financial large language models (FinLLMs). ...

Applying Reinforcement Learning to Option Pricing and Hedging ArXiv ID: 2310.04336 “View on arXiv” Authors: Unknown Abstract This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin (2017). This reinforcement learning approach bridges the traditional Black and Scholes (1973) model with novel artificial intelligence algorithms, enabling option pricing and hedging in a completely model-free and data-driven way. This paper also explores the algorithm’s performance under different state variables and scenarios for a European put option. The results reveal that the model is an accurate estimator under different levels of volatility and hedging frequency. Moreover, this method exhibits robust performance across various levels of option’s moneyness. Lastly, the algorithm incorporates proportional transaction costs, indicating diverse impacts on profit and loss, affected by different statistical properties of the state variables. ...

Efficient option pricing in the rough Heston model using weak simulation schemes ArXiv ID: 2310.04146 “View on arXiv” Authors: Unknown Abstract We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston process derived in [“Bayer and Breneis, arXiv:2309.07023”], and provides weak approximation to the rough Heston process. Numerical experiments show that the new scheme exhibits second order weak convergence, while the computational cost increases linear with respect to the number of time steps. In comparison, existing schemes based on discretization of the underlying stochastic Volterra integrals such as Gatheral’s HQE scheme show a quadratic dependence of the computational cost. Extensive numerical tests for standard and path-dependent European options and Bermudan options show the method’s accuracy and efficiency. ...