Study finds mean reversion strategies perform well on historical data but fail in recent market conditions.
problem Performance of mean reversion strategies in recent market data.
method Empirical investigation of three mean reversion strategies (PAMR, OLMAR, TCO) on historical S&P 500 data and benchmark datasets.
result Mean reversion strategies may fail in recent market conditions, especially with transaction costs.
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean reversion when pricing and hedging options. In particular, we determine both upper and …
The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression ->…
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
Investigates geometric mean reversion process using Lie symmetry method.
problem Describes dynamics of short-term interest rates.
method Lie symmetry method and optimal system of invariant solutions.
result Constructs an optimal system of invariant solutions.
Model explains leverage and mean-reversion in stock prices.
problem Understanding volatility dynamics in financial markets.
method Proposes a local volatility model with piecewise coefficients, estimating parameters using daily stock prices.
result Empirical evidence confirms leverage and mean-reversion effects in stock prices.
Solves optimal control for trading multiple mean-reverting assets.
problem How to construct a portfolio from mean-reverting assets.
method Optimal control problem for power utility agent.
result Nearly explicit solution with properties of optimal solution.
Study fast mean-reversion in large portfolios of stochastic volatility models for accurate loss estimation.
problem Estimating loss from large portfolios of stochastic volatility models with fast mean-reversion.
method Analyzes SPDEs and convergence of stochastic initial-boundary value problems under fast mean-reversion of volatility.
result Accurate estimation of loss distribution using approximate constant volatility models.
Optimal hedging strategies identified for markets with fast-varying volatility.
problem No perfect hedge in markets with fast-varying stochastic volatility.
method Analyzes various delta-type hedging strategies and their performance in a specific asymptotic regime of rapid mean reversion.
result Identifies the `practitioners' delta hedging scheme as optimal in the considered regime of rapid mean reversion.
Improved calibration of HJM models using small volatility approximation.
problem Calibration issues in HJM models with deterministic correlations and mean reversals.
method Use of Small Volatility Approximation in calibration of Multi-Factor HJM models.
result Calibration quality is very good and independent of the number of factors.
Optimizes trading returns using Hurst exponent and Q-learning.
problem Maximizing returns from momentum and mean reversion strategies.
method Classifies assets using Hurst exponent and uses Q-learning to improve trading algorithms.
result Trading with Hurst exponent can achieve higher returns but at higher risk.
This paper applies DRL to mean reversion trading problems.
problem Adopting DRL for financial trading problems.
method Integrates function properties into DRL for mean reversion trading.
result Demonstrates a highly-performant DRL solution for financial decision-making.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Extends a market impact model to include mean-reversion, revealing new order book dynamics.
problem Understanding market impact in a latent order book model.
method Mean-reversion added to a minimal model, analyzed with mean-field assumption.
result New order book dynamics and price impact development shown.
Paper presents online learning for statistical arbitrage without stationarity assumptions.
problem Statistical arbitrage strategies often rely on assumptions that may not hold for non-stationary processes.
method Online learning algorithms for mean reversion models without stationarity assumptions.
result Strong learning guarantees for online learning in non-stationary processes.
The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to …
Algorithm for cryptoasset arbitrage exploiting Bitcoin's leading momentum.
problem Finding profitable trading opportunities in cryptoassets.
method Statistical arbitrage based on mean-reversion and momentum factors.
result Significant altcoin-Bitcoin arbitrage alpha identified.
The leverage effect weakly impacts return distributions, especially for small firms.
problem The leverage effect's impact on return distributions is inconsistent and puzzling.
method Analyzed the determinants of return distributions and proposed an indirect method to measure the interaction effect.
result The interaction effect between leverage and mean-reversion is weak and impacts return distributions mainly for small firms.
Study finds IBS useful for predicting ETF price movements.
problem Predicting short-term price movements in country ETFs.
method Quantitative analysis of historical price data using Mean Reversion.
result IBS can be a useful technical indicator for ETFs.
We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets. In particular, by restricting to domains of bounded volatility, we …
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. We first propose a general problem formulation aimed at finding a portfolio of underlying component assets by optimizing a mean-reversion criterion characterizing the mean-reversion strength, ta…
We find stationary distributions in a financial model with trends and mean-reversion.
problem Financial markets with competing trends and mean-reversion.
method Analytical derivation of stationary distributions in various noise and feedback regimes.
result The distributions are unimodal Gaussians in small noise, small feedback limits, but can be bimodal for stronger trends.
A model-free method analyzes trading strategies using excursion paths.
problem Analyzing risk and return for dynamic trading strategies without probabilistic assumptions.
method Pathwise analysis of trading signals using δ-excursions.
result Continuous paths can be uniquely decomposed into δ-excursions.
Optimal portfolio design for statistical arbitrage in finance.
problem Designing optimal mean-reverting portfolios for statistical arbitrage.
method General problem formulation with investment leverage constraint, followed by successive convex approximation method.
result The proposed model and algorithms effectively construct portfolios with satisfactory mean reversion and variance properties.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
Optimizes a portfolio with mean-reverting assets using Ornstein-Uhlenbeck process.
problem Design a portfolio with high mean reversion and low variance.
method Penalized OU-Likelihood Estimation with specialized algorithm.
result Parsimonious portfolio selection with desirable characteristics.
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump Lévy process and models the characteri…
Black's intuition is supported: prices are roughly twice value over years.
problem Understanding market trends and mean-reversion over different time frames.
method Analyzing medium-term and long-term market behavior through trend-following and fundamentalist behaviors.
result Prices tend to be off by a factor of 2 over years, with mean-reversion tempering market exuberance.
Study shows price bubbles can exist even with heterogeneous beliefs.
problem Equilibrium price formation in markets with different belief groups.
method Analyzes continuous time asset trading with heterogeneous investors and mean reverting asset.
result Price bubbles may not form even with heterogeneous beliefs, contrary to initial expectations.
Pairs trading strategy fails to outperform market benchmarks, but performs well during bear markets.
problem The validity of pairs trading as a profitable strategy in modern markets.
method Used common distance and cointegration methods on US equities from 1990 to 2020, including the Covid-19 crisis.
result The pairs trading strategy does not consistently outperform market benchmarks, but performs well during bear markets.
Optimal trading strategy for microstructure mean reversion in seconds.
problem Trading in seconds when mid price has a mean-reverting error around an efficient price.
method Solves for trading rule maximizing long-run profit rate, accounting for bid-ask spread and mean reversion.
result The optimal trading strategy involves buying when the gap is within a certain range and selling outside, with profit rate dependent on spread and gap standard deviation.
New model for electricity pricing captures mean reversion and jumps.
problem Capturing mean reversion and jumps in electricity market prices.
method Exponential functional of a jump Lévy process, partial integro-differential equation (PIDE), finite differences method.
result European option value is the unique viscosity solution of a PIDE.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Optimal trend-following strategy uses simple EMA, avoiding complex cherry-picked signals.
problem Cherry-picking signals for trend-following strategies.
method Simple EMA for trend capture, avoiding complex indicators.
result Simple EMA is optimal for capturing trend, complex indicators are risky.
Optimal trading strategy using LQR framework with price mean-reversion.
problem Developing a dynamic trading strategy in a market with linear and quadratic costs.
method Model Predictive Control (MPC) approach to optimize trading curve with positivity constraints.
result Optimal trading curve reacts opportunistically to price changes while satisfying constraints.
We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random per…
This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \[ dR_t= (θ+σα(R_t, t))R_t dt +σR_t dB_t \] with an initial value R0=r0∈R, where θ∈R and σ>0 are constants, and the mean correction function $α:\mathbb{R}\times[0,\infty)\to α(x,t)\…
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the syste…
The study finds that factor momentum is significant only at short lags compared to stock momentum.
problem Investigating the relationship between factor momentum and stock momentum.
method Replicated earlier findings and conducted a spanning test controlling for stock momentum and factor exposure.
result Factor momentum is significant only at short lags after controlling for stock momentum and factor exposure.
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion…
Optimizes trading large volumes of volatile assets with fast mean-reverting volatility.
problem Challenges of executing large volumes of illiquid or volatile assets.
method Modeling uncertain volatility and liquidity with fast mean-reverting dynamics, using singular perturbation arguments and high-frequency data.
result Approximately optimal trade execution strategies under fast mean-reversion.
Study risk-sharing equilibria with general transaction costs, proving mean-reversion of returns.
problem Analyzing risk-sharing equilibria with general convex transaction costs.
method Infinite-horizon model with linear state dynamics, solved numerically using deep learning.
result Equilibrium returns mean-revert around frictionless counterparts, with different dynamics for quadratic and proportional costs.
We study the profitability of optimal mean reversion trading strategies in the US equity market. Different from regular pair trading practice, we apply maximum likelihood method to construct the optimal static pairs trading portfolio that best fits the Ornstein-Uhlenbeck process, and rigorously estimate the parameters.…
A new model reconciles rough volatility and jumps.
problem Combining rough volatility and jump processes.
method Developed a reversionary Heston model with fast mean reversions and large vol-of-vols.
result The reversionary Heston model converges to Lévy jump processes for certain values of the parameter.
A new test evaluates risk estimation accuracy using probability integral transform.
problem Measuring the accuracy of financial market risk estimations.
method Probability Integral Transform (PIT) of ex post realized returns against ex ante probability distributions.
result The new test shows the importance of capturing the dynamic of financial markets.
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associ…
Hybrid AI system combines technical, sentiment analysis for adaptive equity trading.
problem Traditional trading strategies fail during high volatility and regime shifts.
method Combines trend-following, mean-reversion, sentiment analysis, machine learning, and market regime filtering.
result Hybrid model achieved 135.49% return on investment over 24 months.