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.
Financial market volatility is a crucial factor for investment planning, option pricing, and financial market regulation, and technology is widely recognized as a key driver of economic growth. In this project, we investigate the co-movement of technology and non-technology sectors over the last two
We synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We also provide simple, closed-form pricing formulas for the Am
We develop a practical framework for identifying and quantifying the hidden layers of risks and optionality embedded in American options by introducing stochasticity into one or more of their underlying determinants. The heuristic approach remedies the problems of conventional pricing systems, which
It is known that the price of call options in the Heston model is determined in a non-unique way. In this paper, this problem is analyzed from the point of view of the existing mathematical theory of uniqueness classes for degenerate parabolic equations. For the special case of degeneracy, a new exa
We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear in
Calculating true volatility is an essential task for option pricing and risk management. However, it is made difficult by market microstructure noise. Particle filtering has been proposed to solve this problem as it favorable statistical properties, but relies on assumptions about underlying market
Models for spin systems known from statistical physics are applied by analogy in econometrics in the form of agent-based models. Researchers suggest that the state variable temperature $T$ corresponds to volatility $σ$ in capital market theory problems. To the best of our knowledge, this has not yet
We revisit the classical Merton consumption–investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $α$-integral, interpolating between Itô, Stratonovich, and related conventions. Holding preferences and the investment opportunity s
The Black-Scholes framework is crucial in pricing a vast number of financial instruments that permeate the complex dynamics of world markets. Associated with this framework, we consider a second-order differential operator $L(x, {\partial_x}) := v^2(x,t) (\partial_x^2 -\partial_x)$ that carries a va
Financial markets convert the incremental arrival of information into asset price changes. In a sandpile model grains of sand represent bits of data, and the size of an avalanche, governed by a scaling law, is linked to price volatility. While this model of self-organized criticality reproduces styl
Random walk models with log-normal outcomes fit local market observations remarkably well. Yet interconnected or recursive structures - layered derivatives, leveraged positions, iterative funding rounds - periodically produce power-law distributed events. We show that the transition from log-normal
In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability of Bitcoin’s price movements, drawing a parallel with traditi
Public finances are one of the fundamental mechanisms of economic governance that refer to the financial activities and decisions made by government entities to fund public services, projects, and operations through assets. In today’s globalized landscape, even subtle shifts in one nation’s public d
The integration of cryptocurrencies into institutional portfolios necessitates the adoption of robust risk modeling frameworks. This study is a part of a series of subsequent works to fine-tune model risk analysis for cryptocurrencies. Through this first research work, we establish a foundational be
In modern times, the cryptocurrency market is one of the world’s most rapidly rising financial markets. The cryptocurrency market is regarded to be more volatile and illiquid than traditional markets such as equities, foreign exchange, and commodities. The risk of this market creates an uncertain co
The inherent volatility and dynamic fluctuations within the financial stock market underscore the necessity for investors to employ a comprehensive and reliable approach that integrates risk management strategies, market trends, and the movement trends of individual securities. By evaluating specifi
``Self-Organised Criticality’’ (SOC) is the mechanism by which complex systems spontaneously settle close to a critical point, at the edge between stability and chaos, and characterized by fat-tailed fluctuations and long-memory correlations. Such a scenario may explain why insignificant perturbat
Standard real options theory predicts delay in exercising the option to invest or deploy when extreme asset volatility or technological uncertainty are present. However, in the current race to develop artificial general intelligence (AGI), sovereign actors are exhibiting behaviors contrary to theore
Over the past 60 years, there has been a gradual increase in the volatility of daily returns for the S&P 500 Index. Hypothetically, suppose that market forces determine daily volatility such that a daily leveraged S&P 500 fund cannot outperform a standard S&P 500 fund in the long run. Then this hypo
The purpose of this study was to examine the relationship between dividend policy and share price volatility with a focus on consumer product companies listed i