Volatility Modeling

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. ...

In traditional finance, systemic risk is often linked to size — the bigger the institution, the bigger the threat. But in crypto? The rules are different. A recent paper from researchers at Jinan University rewrites the forecasting playbook by demonstrating that systemic influence in crypto markets is more about network positioning than market cap. The authors introduce a state-adaptive volatility model that integrates multi-scale realized volatility measures (like semivariance and jump components) with time-varying quantile spillovers, producing a high-resolution view of inter-asset contagion — especially under stress. ...

Most generative models for time series—particularly those borrowed from image generation—treat financial prices like any other numerical data: throw in Gaussian noise, then learn to clean it up. But markets aren’t like pixels. Financial time series have unique structures: they evolve multiplicatively, exhibit heteroskedasticity, and follow stochastic dynamics that traditional diffusion models ignore. In this week’s standout paper, “A diffusion-based generative model for financial time series via geometric Brownian motion,” Kim et al. propose a subtle yet profound twist: model the noise using financial theory, specifically geometric Brownian motion (GBM), rather than injecting it naively. ...