Lévy processes — stochastic processes with jumps — are the bedrock of modern financial modeling. From the Variance Gamma model to the CGMY framework, these models have replaced Brownian motion in capturing the reality of financial returns: asymmetry, fat tails, and sudden discontinuities. But what if we told you these processes don’t just live on probability distributions — they live on manifolds? ...
In a field where LSTMs, transformers, and black-box agents often dominate the conversation, a new framework dares to ask: What if our old tools weren’t wrong, just under-optimized? That’s the central premise behind Technical Indicator Networks (TINs) — a novel architecture that transforms traditional technical analysis indicators into interpretable, trainable neural networks. Indicators, Meet Neural Networks Rather than discarding hand-crafted indicators like MACD or RSI, the TIN approach recasts them as neural network topologies. A Moving Average becomes a linear layer. MACD? A cascade of two EMAs with a subtractive node and a smoothing layer. RSI? A bias-regularized division circuit. The resulting neural networks aren’t generic function approximators; they’re directly derived from the mathematical structure of the indicators themselves. ...
If you’re tired of classical GANs hallucinating financial time series that look right but behave wrong, you’re not alone. Markets aren’t just stochastic — they’re structured, memory-laced, and irrational in predictable ways. A recent paper, Quantum Generative Modeling for Financial Time Series with Temporal Correlations, dives into whether quantum GANs (QGANs) — once considered an esoteric fantasy — might actually be better suited for this synthetic financial choreography. ...
One of the most sacred assumptions in financial modeling is the existence of a traded risk-free asset. It anchors discounting, defines arbitrage boundaries, and supports the edifice of Black–Scholes. But what happens when you remove this pillar? Can we still price options, hedge risk, or extract information about funding conditions? In a striking extension of the Lindquist–Rachev (LR) framework, Ziyao Wang shows that not only is it possible — it may reveal financial dynamics that conventional models obscure. ...
Financial engineers have long sought to tame the volatility surface. From Black-Scholes to Heston, modelers have used parametric tricks to approximate implied volatilities across strikes and maturities. But what happens when the surface refuses to play along—when volatility is rough, the market isn’t Heston, and no closed-form expansion suffices? In today’s article, we explore a signature-based approach from rough path theory that aims to solve this exact problem. The method not only matches the performance of classical asymptotic expansions in well-behaved markets, but even excels when things get bumpy. ...
Why does Bitcoin feel so predictably unpredictable? A recent paper offers a rigorous perspective, arguing that the answer lies in its dual nature: highly regular in the short term, but richly chaotic across time. Using two complementary techniques—Refined Composite Multiscale Sample Entropy (RCMSE) and Multifractal Detrended Fluctuation Analysis (MF-DFA)—the authors dissected the complexity of four major assets: Bitcoin, GBP/USD, gold, and natural gas. Their goal: measure how much structure hides within volatility. ...
The cryptocurrency market is infamous for its volatility, fragmented data, and narrative-driven swings. While traditional deep learning systems crunch historical charts in search of patterns, they often do so blindly—ignoring the social, regulatory, and macroeconomic tides that move crypto prices. Enter MountainLion, a bold new multi-agent system that doesn’t just react to market signals—it reasons, reflects, and explains. Built on a foundation of specialized large language model (LLM) agents, MountainLion offers an interpretable, adaptive, and genuinely multimodal approach to financial trading. ...
Finance may seem like the crown jewel of modern institutions—replete with contracts, algorithms, and global markets. But what if its deepest logic predates banks, money, and even language? In a compelling new paper, Finance as Extended Biology (arXiv:2506.00099), Egil Diau argues that the cognitive substrate of finance is not institutional architecture but reciprocity—a fundamental behavioral mechanism observed in primates and ancient human societies alike. Credit, insurance, token exchange, and investment, he contends, are not designed structures but emergent transformations of this ancient cooperative logic. ...
Markowitz’s mean-variance portfolio theory has long served as a pillar of modern finance, but in its classical form, it assumes a serene world of continuous returns and static market regimes. This serenity, however, shatters when real-world markets swing between boom and bust, triggering sudden and severe asset price shocks. The new paper by Shi and Xu takes a bold step in modeling this turbulence by embedding regime-switching-induced stock price jumps directly into the mean-variance framework. ...
What if picking winning stocks wasn’t about finding isolated outperformers, but about tracing the invisible web of influence that binds the market together? A recent paper proposes exactly that—building portfolios from the market’s structural core, using a dynamic network of directional dependencies extracted from stock returns. At the heart of the approach lies a clever pipeline that fuses econometrics, network theory, and forecasting: Stocks are modeled in pairs using Vector Autoregression (VAR) over rolling 120-day windows. Forecast Error Variance Decomposition (FEVD) quantifies how much each stock influences others, generating a directional dependency matrix. This matrix is symmetrized and distilled into a Minimum Spanning Tree (MST)—a sparse, cycle-free map of the market’s backbone. From this tree, the portfolio selects the top-5 most connected stocks (by degree centrality) in each window—stocks that act as systemic hubs. Then, instead of equal weighting, capital is allocated inversely proportional to each stock’s Value at Risk (VaR) or proportionally to its Sharpe ratio. Stocks with lower downside risk or better risk-adjusted returns receive higher weights. ...