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 investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural networks and show that they outperform LSTMs in most cases, with or
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which assume constant volatility. Constructing the optimal portfolio
The volatility fitting is one of the core problems in the equity derivatives business. Through a set of deterministic rules, the degrees of freedom in the implied volatility surface encoding (parametrization, density, diffusion) are defined. Whilst very effective, this approach widespread in the ind
We present a function-valued stochastic volatility model designed to capture the continuous-time evolution of forward curves in fixed-income or commodity markets. The dynamics of the (logarithmic) forward curves are defined by a Heath-Jarrow-Morton-Musiela stochastic partial differential equation mo
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for moments of any order. Consequently, we propose our moment estimato
Affine Diffusion dynamics are frequently used for Valuation Adjustments (xVA) calculations due to their analytic tractability. However, these models cannot capture the market-implied skew and smile, which are relevant when computing xVA metrics. Hence, additional degrees of freedom are required to c
The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators revealed that most early warning systems are qualitative and causa
The stock market plays a pivotal role in economic development, yet its intricate volatility poses challenges for investors. Consequently, research and accurate predictions of stock price movements are crucial for mitigating risks. Traditional time series models fall short in capturing nonlinearity,
This paper presents an agent based model of an electronic market with two types of trading agents. One type follows a mean reverting strategy and the other, the speculative trader, tracks the maximum realised return over recent trades. The speculators have a distribution of returns concentrated on n
The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use Markovian approximations of the model. Several previous works hav
We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston’s stochastic volatility model. We apply the duality methods developed in previous work to obtain a closed-form expression for the optimal portfolio alloca
Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suf
The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal ($β=0$) SABR model is a popular model choice for interest rates because it allows negative asset values. The option price and delta under the SABR model are typically obtained via asympto
Nonlinear Markov Chains (nMC) are regarded as the original (linear) Markov Chains with nonlinear small perturbations. It fits real-world data better, but its associated properties are difficult to describe. A new approach is proposed to analyze the ergodicity and even estimate the convergence bounds
We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for such (non-Markovian) models concerns efficient numerical schem
We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper
We analyze numerically the performance of Quantum Reservoir Computing (QRC) for statistical and financial problems. We use a reservoir composed of two superconducting islands coupled via their charge degrees of freedom. The key non-linear elements that provide the reservoir with rich and complex dyn
We propose a simple yet robust unsupervised model to detect pump-and-dump events on tokens listed on the Poloniex Exchange platform. By combining threshold-based criteria with exponentially weighted moving averages (EWMA) and volatility measures, our approach effectively distinguishes genuine anomal
In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on reservation prices (in place of the utility function). In this pap