The moments of historic stock returns align with the Heston model, not the multiplicative model.
problem Understanding the distribution of historic stock returns and volatility.
method Comparison of moments with Heston and multiplicative models, analysis of mean realized variance.
result The moments of historic stock returns are better explained by the Heston model than the multiplicative model.
This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient à la Markowitz. It is shown that, when the market coefficients a…
Unified framework combines views and optimization for better portfolio management.
problem Optimizing portfolio weights with dynamic adjustment based on volatility.
method Dynamic sliding window adjusting horizon, factor estimates, BL posterior returns, and weights over time.
result Outperforms dynamic mean-variance optimization without BL views, providing stronger downside risk control.
Study compares VIX and VXO to historic market data volatility distributions.
problem Comparing implied and realized volatility distributions.
method Systematic comparison of VIX and VXO to historic market data, studying distributions and ratios.
result Ratio of implied to realized volatility best fits heavy-tailed and fat-tailed distributions.
Study on distributions of realized and implied volatility, using Generalized Beta distribution.
problem Understanding the differences and relationships between realized and implied volatility distributions.
method Used Generalized Beta distribution to fit distributions of realized variance and implied volatility (VIX, VXO). Analyzed differences and correlations.
result Generalized Beta distribution provides the best fit for realized variance but not for implied volatility indices (VIX, VXO).
Investigates Bitcoin market risk, showing volatility and jumps impact future volatility.
problem Understanding and forecasting the risk dynamics of Bitcoin market.
method Comprehensive investigation using realized volatility and jumps analysis.
result Jumps, especially positive ones, reduce future realized variance; long-term realized variance benefits from modeling jumps.
The study examines how choice of risk measure and volatility estimator affects procyclicality.
problem Understanding the factors affecting procyclicality in risk measure estimation.
method Examined three risk measures (Value-at-Risk, Expected Shortfall, Expectile), realized volatility estimators (sample variance, mean absolute deviation), and two models (iid and GARCH).
result Procyclicality is always present regardless of the choice of risk measure and realized volatility estimator.
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…
BPASGM uses sparse graphical models to optimize portfolio selection.
problem Portfolio optimization in high-dimensional settings with estimation error.
method BPASGM extends BPA to a sparse graphical model, screening assets for diversification.
result BPASGM portfolios outperform standard mean-variance portfolios in risk-adjusted performance.
Bayesian realized-GARCH models forecast financial tail risks using two-sided Weibull distribution.
problem Forecasting financial tail risks in volatile markets.
method Adaptive Bayesian Markov Chain Monte Carlo for estimation and forecasting, incorporating sub-sampled realized range and variance.
result Realized-GARCH models with two-sided Weibull distribution outperform other models in tail risk forecasting.
Investors benefit from long horizons in a market with mean-reverting equity returns.
problem Optimal portfolio choice in a market with mean-reverting risk-free rate and equity risk-premium.
method Mean-variance optimization, Euler-Lagrange equation, Calculus of Variations, spectral problem.
result Optimal policies are characterized by eigenvalues of the lambda-matrix, leading to better risk-return trade-offs for long-term investors.
Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.
problem Analyzing the behavior of short-maturity options on realized variance in local-stochastic volatility models.
method Large deviations theory and variational problems to solve rate functions for different cases.
result Explicit solutions for the rate function in the uncorrelated case and upper/lower bounds and expansions for the correlated case.
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator…
The paper optimizes RV estimation by efficient sampling in time-changed diffusion models.
problem Improving realized variance (RV) estimation in time-changed diffusion models.
method Theoretical analysis and simulations of hitting time and realized business time sampling schemes.
result Realized business time sampling is empirically most efficient for high noise levels.
New framework estimates VaR and ES jointly using Bayesian methods.
problem Joint estimation of Value-at-Risk (VaR) and Expected Shortfall (ES).
method Bayesian Markov Chain Monte Carlo method with measurement equation.
result Proposed models outperform other methods in VaR and ES forecasting.
Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we cond…
Investors with asymmetric information play a game to optimize their portfolios.
problem Two investors with different information levels compete in portfolio selection.
method Modelled as a Stackelberg game with entropy-regularized mean-variance objectives.
result Equilibria exist where follower's strategy depends on leader's actions.
Study shows best fit of squared vol ratios by Beta Prime distribution.
problem Analyzing correlations between VIX, VXO, and realized variances.
method Examined VIX, VXO squared vol correlations and realized variances, fitted with Beta Prime distribution.
result Ratio of squared vol indices best fitted by Beta Prime distribution with parameters dependent on month.
This work creates a CS for non-negative heavy-tailed data with bounded mean.
problem Constructing a confidence sequence for non-negative heavy-tailed data with bounded mean.
method Non-parametric, non-asymptotic lower confidence sequence construction.
result The constructed CS is efficient and can be converted into a closed-interval CS.
Optimizes threshold selection for variance estimation in financial models.
problem Estimating integrated variance in financial models with jumps.
method Optimizes threshold selection using mean and conditional mean square error criteria.
result Proposes a novel method to approximate the optimal threshold.
This paper develops copula-based models for forecasting multivariate realized volatility.
problem Forecasting multivariate realized volatility matrices with hidden dependence structure.
method Copula-based time series models to capture hidden dependence structure and ensure positive definiteness.
result Copula-based models achieve significant performance in volatility matrix forecasting.
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options…
A new perspective on portfolio selection using realized returns.
problem Choosing between two investments with the same expected return.
method Modeling realized returns as random variables and applying the CAPM formula.
result The CAPM formula applies to realized returns, not just their expectations.
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
Flexible framework for modeling predictive distributions of time series
problem Modeling predictive distributions of nonlinear time series
method Generative adversarial networks
result Direct simulation-based approximation to predictive distributions
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoo…
Deep learning approximates SPDE solutions from noise trajectories.
problem Approximating solutions to stochastic partial differential equations (SPDEs).
method Uses neural networks to approximate SPDE solutions based on noise realizations.
result Accurately estimates SPDE solutions and functionals like mean and variance.
We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high a…
Study improves forecast accuracy of daily volatility to enhance portfolio performance.
problem Improving predictability of realized variance from market views.
method High-dimensional machine learning models and low-dimensional factor models used to forecast firm-level volatility.
result Marginal improvements in forecast error lead to significant gains in portfolio performance.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or e…
A new model minimizes investment risk at multiple time points.
problem Minimizing risk in investment portfolios with multiple stopping points.
method Developed a multi-time state mean-variance model using Riccati equations.
result Optimal investment strategies can be derived from a sequence of Riccati equations.
VOLARE provides standardized realized volatility measures from financial data.
problem Lack of standardized realized volatility measures from ultra-high-frequency data.
method Asset-specific pipeline for cleaning and sampling data, providing a wide range of realized estimators.
result Comprehensive set of realized estimators for equities, exchange rates, and futures.
A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.
problem Simplifying mean-variance portfolio theory.
method Introducing the Hansen ratio and extending mean-variance theory.
result The Hansen ratio provides a parsimonious description of the mean-variance efficient frontier.
Develops a GMM method to estimate roughness in stochastic volatility models.
problem Estimating roughness in stochastic volatility models with fractional Brownian motion.
method GMM approach for log-normal models with integrated variance and noisy realized variance.
result Consistent and asymptotically normal parameter estimator with bias correction.
MeanFlow training is unstable due to misusing conditional velocity, leading to variance issues.
problem Unstable training of MeanFlow due to variance problems.
method Theoretical analysis and derivation of optimal coefficient in closed form.
result The optimal coefficient in MeanFlow training minimizes variance but not necessarily quality.
This work addresses unstable MeanFlow training by optimizing a coefficient in the loss function.
problem Unstable training of MeanFlow models with non-decreasing loss and unbounded gradient variance.
method Established a theory attributing the instability to misuse of the conditional velocity field, derived the optimal coefficient, and showed practical realizations.
result Optimal coefficient yields up to 54% improvement in sample quality and monotone FID trend.
Develops Thompson Sampling algorithms for mean-variance bandits.
problem Risk in online decision making systems.
method Thompson Sampling algorithms for mean-variance MAB with comprehensive regret analyses.
result Achieves best known regret bounds for mean-variance MABs and information-theoretic bounds in some regimes.
The paper develops a method for self-normalized inference in adaptive experiments.
problem Adaptive experiments require a fixed horizon for ATE estimation, but propensities can change.
method The method uses self-normalized martingale limit theory to estimate ATE.
result The Studentized statistic is asymptotically N(0,1) at the prespecified horizon.
The paper shows incorrect mean-variance analysis methods should be avoided.
problem Incorrect ex post mean-variance analysis methods in financial studies.
method Illustrates incorrect methods using 2014 biotech ETF data.
result Ex post mean-variance analysis should not be done as generally practiced.
Proposes a Structural Matrix Autoregressive model for joint analysis of asset returns, realized volatility, and trading volume.
problem Joint analysis of asset returns, realized volatility, and trading volume
method Structural Matrix Autoregressive model
result Volatility is primary driver of trading activity, with informational shocks incorporated through price variability.
Bayesian realized EGARCH models improve tail risk forecasting.
problem Forecasting tail risks in financial markets.
method Developed a Bayesian framework for realized EGARCH models, incorporating multiple realized volatility measures and using robust adaptive Metropolis algorithm for estimation.
result Standardized skewed Student-t distribution and sub-sampled realized range models outperform other models in tail risk forecasting.
Study finds short-term instability in financial ARCH models.
problem Short-term stability of financial ARCH models.
method Analyzes quadratic ARCH processes using historical data and empirical innovations.
result Empirical innovations have variance significantly above 1, indicating short-term instability.
This paper explores the harmonic mean of implied volatility and its relation to local volatility.
problem Understanding the relationship between implied volatility and local volatility.
method Investigates the harmonic mean of a positive function for any fixed maturity, linking it to Fukasawa's invertible map.
result The short-dated implied volatility approaches the arithmetic mean of the local volatility in a new coordinate system.
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
problem Finding optimal portfolios under mean-risk criteria for general distributions.
method Using normal mean-variance mixture (NMVM) distributions, the paper derives closed-form expressions for mean-risk frontiers by optimizing a Markowitz model with adjusted return vectors.
result Closed-form solutions for mean-risk portfolios are found for return vectors following NMVM distributions.