Semi-analytical pricing of options written on SOFR futures ArXiv ID: 2409.04903 “View on arXiv” Authors: Unknown Abstract In this paper, we propose a semi-analytical approach to pricing options on SOFR futures where the underlying SOFR follows a time-dependent CEV model. By definition, these options change their type at the beginning of the reference period: before this time, this is an American option written on a SOFR forward price as an underlying, and after this point, this is an arithmetic Asian option with an American style exercise written on the daily SOFR rates. We develop a new version of the GIT method and solve both problems semi-analytically, obtaining the option price, the exercise boundary, and the option Greeks. This work is intended to address the concern that the transfer from LIBOR to SOFR has resulted in a situation in which the options of the key money market (i.e., futures on the reference rate) are options without any pricing model available. Therefore, the trading in options on 3M SOFR futures currently ends before their reference quarter starts, to eliminate the final metamorphosis into exotic options. ...

Pricing and hedging of decentralised lending contracts ArXiv ID: 2409.04233 “View on arXiv” Authors: Unknown Abstract We study the loan contracts offered by decentralised loan protocols (DLPs) through the lens of financial derivatives. DLPs, which effectively are clearinghouses, facilitate transactions between option buyers (i.e. borrowers) and option sellers (i.e. lenders). The loan-to-value at which the contract is initiated determines the option premium borrowers pay for entering the contract, and this can be deduced from the non-arbitrage pricing theory. We show that when there are no market frictions, and there is no spread between lending and borrowing rates, it is optimal to never enter the lending contract. Next, by accounting for the spread between rates and transactional costs, we develop a deep neural network-based algorithm for learning trading strategies on the external markets that allow us to replicate the payoff of the lending contracts that are not necessarily optimally exercised. This allows hedge the risk lenders carry by issuing options sold to the borrowers, which can complement (or even replace) the liquidations mechanism used to protect lenders’ capital. Our approach can also be used to exploit (statistical) arbitrage opportunities that may arise when DLP allow users to enter lending contracts with loan-to-value, which is not appropriately calibrated to market conditions or/and when different markets price risk differently. We present thorough simulation experiments using historical data and simulations to validate our approach. ...

Optimal position-building strategies in competition ArXiv ID: 2409.03586 “View on arXiv” Authors: Unknown Abstract This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are trading strategies and traders try to devise best-response strategies to their adversaries. In this setup trading is guided by a desire to minimize the total cost of trading arising from a mixture of temporary and permanent market impact caused by the aggregate level of trading including the trader and the competition. We describe a notion of equilibrium strategies, show that they exist and provide closed-form solutions. ...

Pricing American Options using Machine Learning Algorithms ArXiv ID: 2409.03204 “View on arXiv” Authors: Unknown Abstract This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to adequately address the complexities of American options, which include the ability for early exercise and non-linear payoff structures. By leveraging Monte Carlo methods in conjunction Least Square Method machine learning was used. This research aims to improve the accuracy and efficiency of option pricing. The study evaluates several machine learning models, including neural networks and decision trees, highlighting their potential to outperform traditional approaches. The results from applying machine learning algorithm in LSM indicate that integrating machine learning with Monte Carlo simulations can enhance pricing accuracy and provide more robust predictions, offering significant insights into quantitative finance by merging classical financial theories with modern computational techniques. The dataset was split into features and the target variable representing bid prices, with an 80-20 train-validation split. LSTM and GRU models were constructed using TensorFlow’s Keras API, each with four hidden layers of 200 neurons and an output layer for bid price prediction, optimized with the Adam optimizer and MSE loss function. The GRU model outperformed the LSTM model across all evaluated metrics, demonstrating lower mean absolute error, mean squared error, and root mean squared error, along with greater stability and efficiency in training. ...

Signature of maturity in cryptocurrency volatility ArXiv ID: 2409.03676 “View on arXiv” Authors: Unknown Abstract We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the $Q$ factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices. ...

Comparative Study of Long Short-Term Memory (LSTM) and Quantum Long Short-Term Memory (QLSTM): Prediction of Stock Market Movement ArXiv ID: 2409.08297 “View on arXiv” Authors: Unknown Abstract In recent years, financial analysts have been trying to develop models to predict the movement of a stock price index. The task becomes challenging in vague economic, social, and political situations like in Pakistan. In this study, we employed efficient models of machine learning such as long short-term memory (LSTM) and quantum long short-term memory (QLSTM) to predict the Karachi Stock Exchange (KSE) 100 index by taking monthly data of twenty-six economic, social, political, and administrative indicators from February 2004 to December 2020. The comparative results of LSTM and QLSTM predicted values of the KSE 100 index with the actual values suggested QLSTM a potential technique to predict stock market trends. ...

Fitting an Equation to Data Impartially ArXiv ID: 2409.02573 “View on arXiv” Authors: Unknown Abstract We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according to which variable is chosen as being dependent, and the dependent variable is unrealistically assumed to be the only variable which has any measurement error (noise). We present a very general method for estimating a linear functional relationship between multiple noisy variables, which are treated impartially, i.e. no distinction between dependent and independent variables. The data are not assumed to follow any distribution, but all variables are treated as being equally reliable. Our approach extends the geometric mean functional relationship to multiple dimensions. This is especially useful with variables measured in different units, as it is naturally scale-invariant, whereas orthogonal regression is not. This is because our approach is not based on minimizing distances, but on the symmetric concept of correlation. The estimated coefficients are easily obtained from the covariances or correlations, and correspond to geometric means of associated least squares coefficients. The ease of calculation will hopefully allow widespread application of impartial fitting to estimate relationships in a neutral way. ...

Fundamental properties of linear factor models ArXiv ID: 2409.02521 “View on arXiv” Authors: Unknown Abstract We study conditional linear factor models in the context of asset pricing panels. Our analysis focuses on conditional means and covariances to characterize the cross-sectional and inter-temporal properties of returns and factors as well as their interrelationships. We also review the conditions outlined in Kozak and Nagel (2024) and show how the conditional mean-variance efficient portfolio of an unbalanced panel can be spanned by low-dimensional factor portfolios, even without assuming invertibility of the conditional covariance matrices. Our analysis provides a comprehensive foundation for the specification and estimation of conditional linear factor models. ...

MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model ArXiv ID: 2409.07486 “View on arXiv” Authors: Unknown Abstract Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite significant efforts to build real-world simulators, the application of generative models to virtual worlds, like financial markets, remains under-explored. In financial markets, generative models can simulate complex market effects of participants with various behaviors, enabling interaction under different market conditions, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the domain-specific need for realistic, interactive and controllable order generation. Key observations include LMM’s strong scalability across data size and model complexity, and MarS’s robust and practicable realism in controlled generation with market impact. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment, thus demonstrating MarS’s “paradigm shift” potential for a variety of financial applications. We release the code of MarS at https://github.com/microsoft/MarS/. ...

MoA is All You Need: Building LLM Research Team using Mixture of Agents ArXiv ID: 2409.07487 “View on arXiv” Authors: Unknown Abstract Large Language Models (LLMs) research in the financial domain is particularly complex due to the sheer number of approaches proposed in literature. Retrieval-Augmented Generation (RAG) has emerged as one of the leading methods in the sector due to its inherent groundedness and data source variability. In this work, we introduce a RAG framework called Mixture of Agents (MoA) and demonstrate its viability as a practical, customizable, and highly effective approach for scaling RAG applications. MoA is essentially a layered network of individually customized small language models (Hoffmann et al., 2022) collaborating to answer questions and extract information. While there are many theoretical propositions for such an architecture and even a few libraries for generally applying the structure in practice, there are limited documented studies evaluating the potential of this framework considering real business constraints such as cost and speed. We find that the MoA framework, consisting of small language models (Hoffmann et al., 2022), produces higher quality and more grounded responses across various financial domains that are core to Vanguard’s business while simultaneously maintaining low costs. ...