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 consider the Heston model with perfect negative spot–variance correlation and its one-dimensional local-volatility projection. Let $I_T^{\mathrm H}$ and $I_T^{\mathrm{LV}}$ denote their respective integrated variances over $[0,T]$. We establish the inequality [ \mathbb{E}\bigl[(I_T^{\mathrm H}-
We study the infinite-horizon optimal investment and consumption problem in a general class of continuous financial markets, where uncertainty is driven by a continuous non-decreasing stochastic clock representing accumulated variance. This framework encompasses classical Markovian and non-Markovian
We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the $G$-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic $G$-BSDE for the logarithmic price. Under suita
We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function. As a by-product, we strengthen the one-half rule of the implied volatility skew
Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic volatility inside stochastic local volatility models.
We develop a theoretical framework that aims to link micro-level option hedging and stock-specific factor exposure with macro-level market turbulence and explain endogenous volatility amplification during gamma-squeeze events. By explicitly modeling market-maker delta-neutral hedging and incorporati
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the Heath-Jarrow-Morton-Musiela framework as solution to a stochastic pa
The optimal asset allocation between risky and risk-free assets is a persistent challenge due to the inherent volatility in financial markets. Conventional methods rely on strict distributional assumptions or non-additive reward ratios, which limit their robustness and applicability to investment go
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz’s Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most notably, the Markovian nature of price dynamics-that often fail t
In this paper, we investigate mean-variance (MV) portfolio selection problems with jumps in a regime-switching financial model. The novelty of our approach lies in allowing not only the market parameters – such as the interest rate, appreciation rate, volatility, and jump intensity – to depend on th
Models for spin systems, known from statistical physics, are applied analogously in econometrics in the form of agent-based models. The models discussed in the econophysics literature all use the state variable $T$, which, in physics, represents the temperature of a system. However, there is little
This paper addresses the approximation of the local volatility function in the Cheyette interest rate model. Its main contribution is an explicit analytical formula for approximating local volatility, derived by extending the classical Dupire framework to interest rate models. In particular, an impl
In [“Han & Schied, 2023, \textit{“arXiv 2307.02582”}”], an easily computable scale-invariant estimator $\widehat{"\mathscr{R"}}^s_n$ was constructed to estimate the Hurst parameter of the drifted fractional Brownian motion $X$ from its antiderivative. This paper extends this convergence result by pr
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we demonstrate that the price process is a true martingale if
We consider a microstructure foundation for rough volatility models driven by Poisson random measures. In our model the volatility is driven by self-exciting arrivals of market orders as well as self-exciting arrivals of limit orders and cancellations. The impact of market order on future order arri
We study small-time central limit theorems for stochastic Volterra integral equations with Hölder continuous coefficients and general locally square integrable Volterra kernels. We prove the convergence of the finite-dimensional distributions, a functional CLT, and limit theorems for smooth transfor
In the realm of option pricing, existing models are typically classified into principle-driven methods, such as solving partial differential equations (PDEs) that pricing function satisfies, and data-driven approaches, such as machine learning (ML) techniques that parameterize the pricing function d
Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among locations; that is, if two locations are in close proximity,
Engle and Russell (1998, Econometrica, 66:1127–1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarit
Herding, where investors imitate others’ decisions rather than relying on their own analysis, is a prevalent phenomenon in financial markets. Excessive herding distorts rational decisions, amplifies volatility, and can be exploited by manipulators to harm the market. Traditional regulatory tools, su