arXiv · arXiv q-fin · 2026
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang
arXiv · arXiv q-fin · 2026
Volatility is the language in which finance often describes risk, but it is not the language in which institutions experience risk. Allocators live through drawdowns, liquidity needs, spending rules, rebalance decisions, board oversight, and the interval between a prior high-water mark and full recovery. This paper develops a path-dependent framework for asymmetric volatility management. The arithmetic of recovery is…
Gregory A. Fanous
arXiv · arXiv q-fin · 2026
We develop a signature-based framework for optimal execution in statistical arbitrage strategies with path-dependent predictive signals. Both the alpha process and the trading speed are modelled as linear functionals of the truncated signature of a time-augmented market path, placing signal generation and execution on the same truncated signature basis. This allows the trading rule to react to the realised history of…
Gianmarco Morbelli, Sven Karbach, Mike Derksen
arXiv · arXiv q-fin · 2025
Volatility forecasting in financial markets is a topic that has received more attention from scholars. In this paper, we propose a new volatility forecasting model that combines the heterogeneous autoregressive (HAR) model with a family of path-dependent volatility models (HAR-PD). The model utilizes the long- and short-term memory properties of price data to capture volatility features and trend features. By integra…
Xiangdong Liu, Sicheng Fu, Shaopeng Hong
arXiv · arXiv q-fin · 2023
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional Itô formula developed by [Viens, F., & Zhang, J. (2019). A martingale approach for fractional Brownian motions and related path dependent PDEs. Ann. Appl. Probab.]. We then leverage these tools …
Ofelia Bonesini, Antoine Jacquier, Alexandre Pannier
arXiv · arXiv q-fin · 2020
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible beca…
Enrico Biffis, Fausto Gozzi, Cecilia Prosdocimi
arXiv · arXiv q-fin · 2018
Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper…
Ioannis Karatzas, Donghan Kim
arXiv · arXiv q-fin · 2022
We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral (every self-financing strategy is a gradient) and that generic domain of functional calculus is inherently arbitrage-free. We then consider the proble…
Henry Chiu, Rama Cont
arXiv · arXiv · 2026
We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve he…
Christian P. Fries
arXiv · arXiv · 2026
Foundation models have transformed domains from language to genomics by learning general-purpose representations from large-scale, heterogeneous data. We introduce TradeFM, a 524M-parameter generative Transformer that brings this paradigm to market microstructure, learning directly from billions of trade events across >9K equities. To enable cross-asset generalization, we develop scale-invariant features and a univer…
Maxime Kawawa-Beaudan, Srijan Sood, Kassiani Papasotiriou, Daniel Borrajo, Manuela Veloso
arXiv · arXiv · 2025
We develop a rigorous walk-forward validation framework for algorithmic trading designed to mitigate overfitting and lookahead bias. Our methodology combines interpretable hypothesis-driven signal generation with reinforcement learning and strict out-of-sample testing. The framework enforces strict information set discipline, employs rolling window validation across 34 independent test periods, maintains complete int…
Gagan Deep, Akash Deep, William Lamptey
arXiv · arXiv · 2025
The tokenization of real-world assets (RWAs) promises to transform financial markets by enabling fractional ownership, global accessibility, and programmable settlement of traditionally illiquid assets such as real estate, private credit, and government bonds. While technical progress has been rapid, with over \$25 billion in tokenized RWAs brought on-chain as of 2025, liquidity remains a critical bottleneck. This pa…
Rischan Mafrur
arXiv · arXiv · 2020
We coin the term *Protocols for Loanable Funds (PLFs)* to refer to protocols which establish distributed ledger-based markets for loanable funds. PLFs are emerging as one of the main applications within Decentralized Finance (DeFi), and use smart contract code to facilitate the intermediation of loanable funds. In doing so, these protocols allow agents to borrow and save programmatically. Within these protocols, inte…
Lewis Gudgeon, Sam M. Werner, Daniel Perez, William J. Knottenbelt
arXiv · arXiv · 2019
This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in fav…
Zbigniew Palmowski, Budhi Surya
arXiv · arXiv · 2019
In this paper, we propose a methodology based on piece-wise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dy…
Guglielmo D'Amico, Filippo Petroni, Philippe Regnault, Stefania Scocchera, Loriano Storchi
arXiv · arXiv · 2017
We present a version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an $L^p$-setting for $ 1 \leq p < \infty$. This extends the results of Yuri Kabanov and Christophe Stricker \cite{KS:06} to continuous time and to a large financial market setting, however, still preserving the simplicity of the discrete time setting. On the other hand it general…
Christa Cuchiero, Irene Klein, Josef Teichmann
arXiv · arXiv · 2016
In this paper, we search whether the Benford's law is applicable to monitor daily changes in sovereign Credit Default Swaps (CDS) quotes, which are acknowledged to be complex systems of economic content. This test is of paramount importance since the CDS of a country proxy its health and probability to default, being associated to an insurance against the event of its default. We fit the Benford's law to the daily ch…
Marcel Ausloos, Rosella Castellano, Roy Cerqueti
arXiv · arXiv · 2015
For the last two decades, most financial markets have undergone an evolution toward electronification. The market for corporate bonds is one of the last major financial markets to follow this unavoidable path. Traditionally quote-driven i.e., dealer-driven) rather than order-driven, the market for corporate bonds is still mainly dominated by voice trading, but a lot of electronic platforms have emerged. These electro…
Jean-David Fermanian, Olivier Guéant, Jiang Pu