Study optimal trading strategies for mean-reverting spreads using integral equations.
problem Optimal timing for trading mean-reverting price spreads.
method Utilized local time-space calculus and nonlinear integral equations of Volterra-type.
result Derived optimal boundaries for trading strategies.
Optimal timing strategy for mean-reverting price spreads.
problem Trading price spreads with mean-reverting characteristics.
method Sequential optimal stopping framework with refined signature method.
result Precise entry and exit timings that maximize gains.
A Monte Carlo method for pairs trading on mean-reverting spreads with Lévy processes.
problem Trading on mean-reverting spreads with flexible models.
method Monte Carlo simulation with variance gamma and alpha-gamma driving processes.
result Optimal trading strategies are affected by model parameters and correlation.
Paper proposes an efficient MM method for optimizing mean-reverting portfolios in finance.
problem Optimizing mean-reverting portfolios in financial markets considering mean-reversion strength, variance, and investment constraints.
method Majorization-Minimization (MM) method.
result The proposed method significantly outperforms other methods in financial market simulations.
Model prices sovereign contingent convertible bonds during crises.
problem Pricing Sovereign Contingent Convertible bonds (S-CoCo) during crises.
method Model CDS spread regime switching as a hidden Markov process, coupled with a mean-reverting stochastic process. Use Longstaff-Schwartz American option pricing framework for simulation.
result Computed future state contingent S-CoCo prices for risk management.
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is…
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
Study examines returns of Asian ADRs, finding mean-reverting patterns and developing trading strategies.
problem Analyzing returns of Asian ADRs in asynchronous markets.
method Dissected returns into intraday and overnight components, fitted to Ornstein-Uhlenbeck process, developed pairs trading strategies.
result Consistent positive payoffs in pairs trading strategies exploiting mean-reverting ADR-SPY spreads.
Study of volume dynamics at market spread in Bitcoin/USD.
problem Understanding the statistical properties of order volumes in financial markets.
method Examined the dynamical properties of volume available at the spread, focusing on mean reversion, asymmetry, and clustering.
result Evidence of mean reverting volume changes and strong asymmetries in sell and buy orders.
Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…
This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat positi…
Study reveals patterns in US stock opening and closing auctions.
problem Investigating the dynamics of US equities opening and closing auctions.
method Analysis of historical data and conditional analysis of auction prices.
result Opening and closing auctions have distinct price reactions to order placements/cancellations.
The paper introduces a new pairs trading model using nonlinear and non-Gaussian state-space models.
problem Developing a robust trading strategy for pairs of assets with non-Gaussian and heteroskedastic innovations.
method A nonlinear and non-Gaussian state-space model for the spread between two assets, with mean reversion modeled as a mean-reverting process.
result The new trading strategy yields significantly higher returns and Sharpe ratios compared to existing methods.
Optimizes sparse mean-reverting portfolios for higher returns.
problem Finding optimal stock weights for mean-reverting portfolios.
method Transformed optimization problem into SDP, added constraints.
result Sparse mean-reverting portfolios provide higher returns with transaction costs.
Based on the concept of self-decomposable random variables we discuss the application of a model for a pair of dependent Poisson processes to energy facilities. Due to the resulting structure of the jump events we can see the self-decomposability as a form of cointegration among jumps. In the context of energy faciliti…
Develops a statistical arbitrage strategy with stop-loss and leverage for energy markets.
problem Optimizing trading strategies in high-frequency energy markets with stop-loss and leverage.
method Analytical approach using mean-reverting processes and optimal trading strategies.
result Analytical expressions for expected First-Exit-Times and long-run returns of the strategy.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
The paper models default probabilities and total defaults in credit portfolios using a contagion process with self-exciting jumps.
problem Modeling default probabilities and total defaults in credit portfolios to mitigate credit risk.
method Developed a contagion process with self-exciting jumps to model credit events and derive closed-form expressions for default probabilities and total defaults.
result The proposed framework captures the feedback effect and can be used to price synthetic CDOs.
The paper reconciles rough volatility with fast mean reverting models.
problem Empirical evidence of rough volatility contradicts fast mean reverting models.
method Analyzes mean reverting rough volatility and compares it to fast mean reverting Markov volatilities.
result Price impact of rough volatility coincides with fast mean reverting models.
Modified model prevents volatility from approaching zero.
problem Volatility in the Gatheral model can approach zero, making it statistically indistinguishable.
method Proposed a modified model with Skorokhod reflection to prevent volatility from approaching zero.
result The modified model prevents volatility from approaching zero, preserving the model's flexibility.
Shorting IG ETFs can hedge bond portfolios during market drawdowns effectively.
problem Managing downside risk in bond portfolios during market crises.
method Constructing three signals (Momentum, Liquidity, Credit) to dynamically hedge short IG positions.
result Dynamic hedge removes when predicted hedged return mean reverts, achieving higher returns and Sortino ratios.
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.
The paper designs mean-reverting portfolios with budget constraints.
problem Designing mean-reverting portfolios with a budget constraint.
method General problem formulation, optimization of mean-reversion criterion, consideration of portfolio variance, and investment budget constraint. Proposed specific problems and efficient algorithms.
result Our methods generate consistent profits and outperform traditional and benchmark methods.
Mean-reverting assets are one of the holy grails of financial markets: if such assets existed, they would provide trivially profitable investment strategies for any investor able to trade them, thanks to the knowledge that such assets oscillate predictably around their long term mean. The modus operandi of cointegratio…
The paper models exchange rate risk premium using mean-reverting dynamics.
problem Empirical failure of uncovered interest parity (UIP).
method Modeling risk premium using Ornstein-Uhlenbeck (OU) process embedded in stochastic differential equation for exchange rate.
result The model shows strong predictive performance at short and long horizons, but underperforms at intermediate horizons.
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.
This paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a pair to short the outperforming stock and to long the underperforming one. Such…
The paper studies efficient simulation methods for financial firm values under fast mean-reverting volatility.
problem Estimating the probability of firm default under fast mean-reverting stochastic volatility models.
method Approximations using ergodic averages and central limit theorem corrections for efficient simulation.
result Accuracy of approximations assessed through numerical simulation and payoff function estimation.
The paper analyzes optimal portfolio allocation under a fast mean-reverting fractional stochastic environment.
problem Optimal portfolio allocation under a fractional stochastic environment with long-range dependence.
method Analyzes the nonlinear optimal portfolio allocation problem using a stationary fractional Ornstein-Uhlenbeck process with fast mean-reverting.
result Establishes asymptotic optimality of zeroth order trading strategies and general utility functions within specific families of admissible strategies.
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price…
Study pairs trading strategy with uncertain drift and penalized risk.
problem Optimizing pairs trading strategy with uncertain drift and risk penalty.
method Model pairs trading as a Gaussian mean-reverting process with a Markov chain, use stochastic filtering theory, and solve for logarithmic utility function.
result Characterize optimal strategies and value functions under full and partial information, showing certainty equivalence principle.
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.
The paper solves complex swing option pricing equations with numerical methods.
problem Valuation of swing options with jumps under a mean-reverting model.
method Proposes second-order numerical methods to solve PIDEs convection-dominated and with nonlocal integral terms.
result Numerical methods confirm second-order convergence behavior.
Optimal purchasing policy for mean-reverting items with a finite deadline.
problem Minimizing cost of purchasing and holding mean-reverting items within a fixed time.
method Proved optimal policy as a time-variant threshold function, constructed with dynamic programming.
result Explicit equations for crossing time probability and overshoot expectation.
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations wi…
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of min(3α−1,1) for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model. Trading styles affect long-run variance of asset prices, increasing under trend-following and decreasing under mean-reverting.
problem Understanding how different trading styles impact the long-run variance of asset prices.
method Probabilistic models designed to capture the direction of trading were used.
result Trading styles increase long-run variance under trend-following and decrease it under mean-reverting conditions.
New numerical method for non-linear asset price model with CEV volatility.
problem Describing stochastic volatility in asset price dynamics.
method Proposes a mean-reverting theta-rho model with CEV volatility, constructs a truncated EM method.
result Truncated EM solutions can evaluate path-dependent financial products.
Paper presents fast methods for pricing energy derivatives using mean-reverting jump-diffusion models.
problem Pricing energy derivatives with mean-reverting and occasional spikes.
method Exact and fast simulation of spot price dynamics using Ornstein-Uhlenbeck and jump-diffusion processes.
result Apparent computational advantages of the proposed procedures for pricing Asian options, gas storages, and swings.
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.
Develops a new trading strategy for statistical arbitrage with path-dependent signals.
problem Optimal execution in statistical arbitrage strategies with dynamic predictive signals.
method Signature-based framework modeling alpha and trading speed as linear functionals of truncated signature of market path.
result Fitted policy achieves higher return on turnover compared to a z-score benchmark.
Study on market data relaxation and correlations in mean-reverting models.
problem Analyzing relaxation and correlations in market data using mean-reverting models.
method Derived closed-form expressions for correlation functions and leverage for various models, applied eigenvalue analysis for the Heston model, tested findings on historic financial markets data.
result Agreement between general analysis and Heston model's eigenvalue analysis for correlation function.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
problem Calibration of mean-reverting SABR models to equity volatilities.
method Derive closed-form approximations using a CIR process for volatility, lognormal process for volatility, and CIR process for squared volatility. Calibrate to empirical volatilities using a computer algebra system.
result Calibrated mean-reverting SABR models provide excellent fits to equity volatilities with only five parameters per surface.
Hidden Markov model predicts profitable statistical arbitrage in Shanghai crude oil futures.
problem Statistical arbitrage opportunities in international crude oil futures markets.
method Hidden Markov model for cointegration spread, mean-reverting regime-switching process.
result Statistical arbitrage strategies involving Shanghai crude oil futures are profitable.
The paper analyzes optimal timing to sell assets under different price dynamics and utility functions.
problem Optimal timing to sell risky assets under different price dynamics and risk preferences.
method Two stochastic models (trending and mean-reverting) and three utility functions (exponential, power, log) are considered to derive optimal thresholds and certainty equivalents.
result The timing option can make the investor's value function and certainty equivalent non-concave in price.
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a …
Two new models improve option valuation for negative or mean reverting futures markets.
problem Valuation of futures contracts with negative underlying prices.
method Proposed two models: Ornstein-Uhlenbeck and continuous time GARCH.
result Improved option values compared to Black 76, especially for negative or mean reverting markets.
Modeling horse race betting odds with Ornstein-Uhlenbeck process.
problem Analyzing how herding and informed bettors affect odds movements.
method Deriving an Ornstein-Uhlenbeck process from vote shares and odds movements data.
result Identified microscopic and macroscopic patterns in odds convergence.