Bayesian model predicts interest rates with short-term accuracy and long-term stability.
problem Improving short- and long-term prediction of time series with temporary non-stationary behavior.
method Time-varying autoregressive model with Bayesian regularization and MCMC inference.
result Model outperforms existing methods in both short and long-term predictions.
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.
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
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.
A new model reduces rating transition matrix estimation errors for small portfolios.
problem Estimating rating transition matrices for small portfolios leads to unreliable and unstable predictions.
method A sparse structural model with three parameters that assumes an autoregressive mean-reverting ability-to-pay process.
result The model produces well-behaved transition probabilities, reducing statistical degrees of freedom and improving reliability.
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.
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.
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.
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…
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. The problem is formulated by optimizing a criterion characterizing the mean-reversion strength of the portfolio and taking into consideration the variance of the portfolio and an investment budg…
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.
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it …
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.
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.
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.
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…
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…
Generating realistic asset-class scenarios from time series and curves
problem Simulating realistic trajectories for asset classes
method Combining parametric and resampling techniques
result More coherent and realistic simulations of yield-curve dynamics
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.
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.
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 …
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.
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X,D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it wi…
Optimizes portfolios in fast mean-reverting markets, achieving asymptotic efficiency.
problem Optimizing portfolios in markets with fast mean-reverting returns and volatility.
method Proposes a zeroth order strategy and uses singular perturbation method for asymptotic optimality.
result Shows asymptotic optimality of the proposed strategy under specific assumptions.
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility sur…
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a use…
A large class of trading strategies focus on opportunities offered by the yield curve. In particular, a set of yield curve trading strategies are based on the view that the yield curve mean-reverts. Based on these strategies' positive performance, a multiple pairs trading strategy on major currency pairs was implemente…
Study on large portfolio losses with correlated volatility processes converging to a stochastic PDE.
problem Large portfolio losses with correlated volatility processes.
method Structural stochastic volatility model, mean-reverting diffusions, stochastic initial-boundary value problem.
result Convergence of empirical measure process to a stochastic PDE solution under certain conditions.
Investors can achieve optimal risk-reward trade-offs with bonds and stocks under mean-reverting stock returns.
problem Optimizing investment strategies with mean-reverting stock returns.
method Calculus of variations to derive the entire family of extremal strategies, not just the optimal ones.
result The value of the portfolio is effectively bounded from below, providing a 'guarantee' on the horizon.
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European opt…
Paper combines latent state space with CRF for improved autoregressive text generation.
problem Autoregressive models expose hidden state trajectory to biases.
method Combines latent state space model with CRF observation model.
result Improved performance on unconditional sentence generation compared to RNN and GAN baselines.
Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling th…
Efficiently improves non-autoregressive sequence models for better translation performance.
problem Heavy inference latency and inconsistent output sentences in non-autoregressive models.
method Incorporates a structured inference module with an efficient CRF approximation and dynamic transition technique.
result Significantly better translation performance (BLEU score 26.80) compared to previous non-autoregressive models.
Optimal control models for limit order trading often assume that the underlying asset price is a Brownian motion since they deal with relatively short time scales. The resulting optimal bid and ask limit order prices tend to track the underlying price as one might expect. This is indeed the case with the model of Avell…
New GP kernels avoid mean reversion without losing smoothness.
problem Pathological behavior in stationary GP regression.
method Improper Gaussian processes with non-positive kernels.
result Stationary, non-reverting covariance functions.
This work proposes an efficient autoregressive model for text generation.
problem The challenge of generating high-quality text with autoregressive models.
method Introduces a cascaded decoding approach using Markov transformers to achieve sub-linear parallel time generation.
result Shows competitive accuracy/speed tradeoff compared to existing methods on five machine translation datasets.
Optimal control problem for firm cash flow with dividend and capital injection strategies.
problem Maximizing dividends while managing capital injections in a firm's cash flow.
method Proved two optimal strategies: mean-reverting dividends with capital injections or no injections until ruin.
result Optimal strategies are dichotomous: either mean-reverting dividends with injections or no injections.
Paper proposes a new method for finding sparse mean reverting portfolios efficiently.
problem Finding sparse mean reverting portfolios from a large number of assets.
method Leverages H-SGDLM data to formulate a quasi-convex minimization problem with a normalisation constraint, solving it with a cyclical coordinate descent algorithm.
result Efficiently computes exact sparse solutions for large asset universes, demonstrating flexibility, speed, and scalability.
Gaussian Processes enhance financial forecasting by predicting mean-reverting time series with probability distributions.
problem Accurate long-term financial predictions with probability distributions.
method Functional and augmented data structures for Gaussian Processes.
result Gaussian Processes offer improved long-term predictions with probability distributions.