Volatility is the most forecastable quantity in finance — unlike returns, it clusters, mean-reverts, and leaves a measurable footprint in high-frequency data. This hub collects the modeling lineage from GARCH through realized volatility built on intraday data, to rough volatility and the modern deep-learning forecasters, along with VIX and variance-risk-premium research.
Because volatility forecasting has real benchmarks, rigor is easier to judge here than elsewhere: a serious paper compares against HAR-RV (the stubborn workhorse baseline) on out-of-sample data, not just against its own ablations. Watch also for the evaluation-loss trap — rankings of volatility models flip depending on whether you score them with MSE, QLIKE, or economic value in an options or risk-targeting strategy, and good papers say so explicitly.
Related hubs: Options & Derivatives, Risk Management, Machine Learning for Forecasting.
We study the impacts of business cycles on machine learning (ML) predictions. Using the S&P 500 index, we find that ML models perform worse during most recessions, and the inclusion of recession history or the risk-free rate does not necessarily improve their performance. Investigating recessions wh
Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a
This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets’ dependencies, especially correlational studies, which in our opinion are beneficial for
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an unknown, time-varying exercise boundary. The Heston model i
We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongs
True Volterra equations are inherently non stationary and therefore do not admit $\textit{genuine stationary regimes}$ over finite horizons. This motivates the study of the finite-time behavior of the solutions to scaled inhomogeneous affine Stochastic Volterra equations through the lens of a weaker
In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Ma
In this paper we study the short-maturity asymptotics of up-and-in barrier options under a broad class of stochastic volatility models. Our approach uses Malliavin calculus techniques, typically used for linear stochastic partial differential equations, to analyse the law of the supremum of the log-
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position’s delta at each point in time over an infinite time horizon, thus taki
Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these changes. Four components-volatility stress testing, stableco
Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for mode
We present here some results for the PDE related to the logHeston model. We present different regularity results and prove a verification theorem that shows that the solution produced via the Feynman-Kac theorem is the unique viscosity solution for a wide choice of initial data (even discontinuous)
We investigate a class of non-Markovian processes that hold particular relevance in the realm of mathematical finance. This family encompasses path-dependent volatility models, including those pioneered by [Platen and Rendek, 2018] and, more recently, by [Guyon and Lekeufack, 2023]. Our study unfold
We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and Henry-Labordère (2022). The method is illustrated with effic
We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asymptotic risk-based prices form a strongly continuous convex mono
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 hi
The Foreign Exchange market is a significant market for speculators, characterized by substantial transaction volumes and high volatility. Accurately predicting the directional movement of currency pairs is essential for formulating a sound financial investment strategy. This paper conducts a compar
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded financial asset price with uncertain volatility. The quantum
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model
The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term lim