Stochastic Correlation Research Articles

Fuzzy Portfolio Selection Using Stochastic Correlation.

The online version contains supplementary material available at 10.1007/s10614-023-10371-w.

Remaining Useful Life Prediction for Multiple Degradation Indicators Systems Considering Stochastic Correlation

Remaining Useful Life Prediction for Multiple Degradation Indicators Systems Considering Stochastic Correlation

A Multi-objective Chance-constrained Information-gap Decision Model for Active Management to Accommodate Multiple Uncertainties in Distribution Networks

The load demand and distributed generation (DG) integration capacity in distribution networks (DNs) increase constantly, and it means that the violation of security constraints may occur in the future. This can be further worsened by short-term power fluctuations. In this paper, a scheduling method based on a multi-objective chance-constrained information-gap decision (IGD) model is proposed to obtain the active management schemes for distribution system operators (DSOs) to address these problems. The maximum robust adaptability of multiple uncertainties, including the deviations of growth prediction and their relevant power fluctuations, can be obtained based on the limited budget of active management. The systematic solution of the proposed model is developed. The max term constraint in the IGD model is converted into a group of normal constraints corresponding to extreme points of the max term. Considering the stochastic characteristics and correlations of power fluctuations, the original model is equivalently reformulated by using the properties of multivariate Gaussian distribution. The effectiveness of the proposed model is verified by a modified IEEE 33-bus distribution network. The simulation result delineates a robust accommodation space to represent the adaptability of multiple uncertainties, which corresponds to an optional active management strategy set for future selection.

Multi-Asset Option Pricing Using Normal Tempered Stable Processes with Stochastic Correlation

In this article, the authors develop a new multi-asset option pricing model where underlying dynamics are assumed to follow the normal tempered stable (NTS) process and its correlation structure evolves over time. The model is constructed by extending the constant correlation term in the previous NTS framework to the stochastic correlation making use of the Ornstein-Uhlenbeck process. We then derive its closed-form solution under the risk-neutral measure and apply it to an empirical study of a quanto option. The in-sample tests and calibration practices justify our model specification reflecting the empirical stylized facts on asset returns such as heavy tails, skewness, kurtosis, and stochastic correlation. Building on the empirical results, we can also identify the presence of stochastic correlation in the risk-neutral world.

Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models

We document five novel empirical findings on the well-known potential ordering drawback associated with the time-varying parameter vector autoregression with stochastic volatility developed by Cogley and Sargent (2005) and Primiceri (2005). First, the ordering does not affect point prediction. Second, the standard deviation of the predictive densities implied by different orderings can differ substantially. Third, the average length of the prediction intervals is also sensitive to the ordering. Fourth, the best ordering for one variable in terms of log-predictive scores does not necessarily imply the best ordering for another variable under the same metric. Fifth, the ordering problem becomes exacerbated in conditional forecasting exercises. Then, we consider three alternative ordering invariant models: a canonical discounted Wishart stochastic volatility model and two dynamic stochastic correlation models. When the forecasting performance of these ordering invariant models is compared to Cogley, Primiceri, and Sargent’s ordering variant model, the former underperforms relative to all orderings and the latter two have an out-of-sample forecasting performance comparable with the median outcomes across orderings.

A hybrid proper orthogonal decomposition-heteroscedastic sparse Gaussian process regression model for evaluating structural reliability with correlated stochastic material properties

Data-driven material models have shown advantages in recent studies since they can directly use the existing data and improve the model performances further when additional data is available. However, few data-driven material models in the previous studies considered the uncertainty and stochastic correlations of the material properties. In this work, the hybrid Proper Orthogonal Decomposition-Heteroscedastic Sparse Gaussian Process Regression (POD-HSGPR) framework is proposed for predicting stochastic material behaviors and their correlation. The two material behaviors case studies on the metal strength and the rock joint behavior have demonstrated that the proposed POD-HSGPR-based stochastic material model can effectively capture the material properties, material uncertainty, and stochastic correlation between the material behaviors directly from the experimental dataset. The proposed POD-HSGPR model is then applied to a rock slope structure problem to investigate the influence of the correlation of material properties on structural behavior. The results indicate that the proposed POD-HSGPR model could effectively quantify the correlation effect in a non-parametric format and avoid the overestimation of structural reliability.

Multi-performance degradation reliability assessment method for a cabin door locking mechanism

A crucial part of the aircraft, the landing gear cabin door locking mechanism directly affects how well the landing gear retracts and how stealthily the aircraft operates. A reliability evaluation approach under multiple deterioration is provided, with a focus on the features of high reliability, small sample, and multiple performance degradation of the locking mechanism. The locking angle of the lock hook and the locking displacement offset of the lock hook are chosen as the characteristic quantities based on the analysis of the factors influencing the life of the locking mechanism; next, the Wiener process is used to model the degradation process of the selected characteristic quantities in order to obtain the failure probability density function for both; then, the multiple performance degradation reliability evaluation model is established using the Copula function, which can precisely and effectively characterize the coupled competitive relationships of multiple performance degradations. This model characterizes the stochastic correlation between the locking angle and the locking displacement of the lock hook. Following that, the Akaike information criteria (AIC) is used to choose the Copula function. Finally, the locking mechanism’s reliability assessment is carried out, as well as the evaluation findings are contrasted with those of the usual technique, which only takes into account a single failure performance characteristic quantity. A series of data analyses led to the conclusion that the approach is more relevant and accurate than that of the conventional method, and that it is not prudent to undervalue its dependability.

A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes

AbstractThis work aims to forecast (over 1, 5, and 15 years) the extremes, the expected value, and the volatility of natural disasters occurrences. To achieve this objective, we adopt a generalized two‐factor square‐root model linking together occurrences and volatility through stochastic correlation (Brownian motion). We use a generalized Pareto distribution (GPD) to forecast the maximum number of occurrences as a measure of value at risk (VaR). The results are checked in terms of accuracy, compared versus some baseline models (i.e., the Poisson process and the extreme value model) and backtested.

Margin requirements based on a stochastic correlation model

AbstractWe demonstrate that margin requirements of central counterparties show a significantly different behavior when calculated with a portfoliowise treatment instead of taking the weighted sum of the margin requirements of the components without accounting for their correlation structures. This is shown via simulating trajectories of a joint stochastic volatility–stochastic correlation model. Results indicate that an unnecessarily large overmargin requirement is set by regulators when the applied risk measure is not calculated via a portfoliowise treatment. Finally, accounting for the correlation structure of the assets during the margining process would not lead to an overly prudent method, nor would it cause greater procyclicality.

Stochastic assessment of frequency support from wind power plants for power system with high wind penetration using correlation between wind farms

The increase of renewable energy use in a power generation decreases the flexibility of power supply. The intermittent and variable nature of renewable resources necessitates the use of a transmission system operator to prepare reserve generating power in case of power imbalance. Unfortunately, the generation and reserve margins of renewable energy generators are often insufficient. To ensure a balanced and resilient power system, surplus power generation from renewable resources must provide frequency support with the essential number of synchronous generators being remained in the network. Assessment of the amount of frequency support power from wind farm became available through forecast and real-time operation planning. However, the exact amount of back-up power that expected to be provided by individual wind farm can be barely determined due to the uncertainty and variation of renewable resources generation. A stochastic method for assessing the required frequency support operation of specific wind power plants is thus proposed in this paper. The stochastic correlation characteristics between a single wind farm and power system stability are applied in this method. The essential metrics for deloading operation and inertia response are calculated using the stochastic correlation model based on copula function.

Analytical Formulas for Conditional Mixed Moments of Generalized Stochastic Correlation Process

This paper proposes a simple and novel approach based on solving a partial differential equation (PDE) to establish the concise analytical formulas for a conditional moment and mixed moment of the Jacobi process with constant parameters, accomplished by including random fluctuations with an asymmetric Wiener process and without any knowledge of the transition probability density function. Our idea involves a system with a recurrence differential equation which leads to the PDE by involving an asymmetric matrix. Then, by using Itô’s lemma, all formulas for the Jacobi process with constant parameters as well as time-dependent parameters are extended to the generalized stochastic correlation processes. In addition, their statistical properties are provided in closed forms. Finally, to illustrate applications of the proposed formulas in practice, estimations of parametric methods based on the moments are mentioned, particularly in the method of moments estimators.

Out-of-sample forecasting of cryptocurrency returns: A comprehensive comparison of predictors and algorithms

Existing evidence shows that daily cryptocurrency returns are predictable by publicly available variables. However, a majority of evidence relies on potentially over-fitted in-sample estimation. This paper provides a comprehensive comparison of predictors and forecasting methods in the literature for out-of-sample return predictions of Bitcoin, Ethereum, and Ripple. We find that (1) well-known in-sample predictors such as investor attention and trading volume fail to produce statistically significant out-of-sample predictability, (2) a change in stochastic correlation with stock markets is the only meaningful predictor with out-of-sample R2 up to 2.69%, 1.71%, and 2.12% for Bitcoin, Ethereum, and Ripple, respectively, and (3) forecasting methods greatly differ in their performances; methods that are inspired by economic mechanism outperform universal forecasting methods such as shrinkage estimators, combination forecasts, monitoring forecasts, and various machine learning algorithms that are commonly used in practice.

Application of RQMC for CDO Pricing with Stochastic Correlations under Nonhomogeneous Assumptions

In consideration of that the correlation between any two assets of the asset pool is always stochastic in the actual market and that collateralized debt obligation (CDO) pricing models under nonhomogeneous assumptions have no semianalytic solutions, we designed a numerical algorithm based on randomized quasi‐Monte Carlo (RQMC) simulation method for CDO pricing with stochastic correlations under nonhomogeneous assumptions and took Gaussian factor copula model as an example to conduct experiments. The simulation results of RQMC and Monte Carlo (MC) method were compared from the perspective of variance changes. The results showed that this numerical algorithm was feasible, efficient, and stable for CDO pricing with stochastic correlation under nonhomogeneous assumptions. This numerical algorithm is expected to be extended to other factor Copula models for CDO pricing with stochastic correlations under nonhomogeneous assumptions.

First-order formalism of holographic Wilsonian renormalization group: Langevin equation

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic renormalization flow of multi-trace operators and stochastic $n$-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS$_6$. What we have found is that the stochastic time $t$ dependent 3-point function obtained from Langevin equation with its Euclidean action being given by $S_E=2I_{os}$ is identical to holographic renormalization group evolution of holographic triple trace operator as its energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi point functions and multi trace operators in each framework.

Computer-assisted stochastic multi-well correlation: Sedimentary facies versus well distality

Computer-assisted stratigraphic correlation can help to produce several scenarios reflecting interpretation uncertainties. In this work, we propose a method which translates sedimentary concepts into a correlation cost for each possible stratigaphic correlation. All these correlation costs are used to populate a cost matrix in order to apply the Dynamic Time Warping algorithm and to compute the n-best correlation sets having the n-least cumulative costs. The proposed cost function reflects prior knowledge about sediment transport direction, and it is tested on two wells penetrating a Middle Jurassic reservoir in the North Sea. Well markers are described by two parameters: (1) the sedimentary facies corresponding to a depositional environment, and (2) the relative distality of the well computed from its position along the sediment transport direction. The main principle of correlation used in this article assumes that a well marker (described by a facies and a distality) cannot be correlated with another well marker described by a depositionally deeper facies at a more proximal position, or a depositionally shallower facies at a more distal position. This approach produces consistent stratigraphic well correlations, and highlights the sensitivity of the solution to the facies zonation and to the relative well distality. Therefore, the proposed rule offers a way to coherently consider chronostratigraphic correlation and the associated uncertainties at the parasequence scale, i.e., at a smaller scale than generally considered in deterministic correlation.

On the application of Wishart process to the pricing of equity derivatives: the multi-asset case

Given the inherent complexity of financial markets, a wide area of research in the field of mathematical finance is devoted to develop accurate models for the pricing of contingent claims. Focusing on the stochastic volatility approach (i.e. we assume to describe asset volatility as an additional stochastic process), it appears desirable to introduce reliable dynamics in order to take into account the presence of several assets involved in the definition of multi-asset payoffs. In this article we deal with the multi asset Wishart Affine Stochastic Correlation model, that makes use of Wishart process to describe the stochastic variance covariance matrix of assets return. The resulting parametrization turns out to be a genuine multi-asset extension of the Heston model: each asset is exactly described by a single instance of the Heston dynamics while the joint behaviour is enriched by cross-assets and cross-variances stochastic correlation, all wrapped in an affine modeling. In this framework, we propose a fast and accurate calibration procedure, and two Monte Carlo simulation schemes.

Emergence of Non-Speculative Demand for Bitcoin: Learning about Stochastic Correlations with Stock Markets

When a new asset keeps changing its narrative, investors find difficulty in classifying and understanding the new asset. Rational investors therefore face unprecedented uncertainty and learn about the joint dynamics to optimize their portfolio accordingly. Bitcoin's digital gold narrative, as a safe haven, best demonstrates this uncertainty-learning behavior. We find that an increase in investors' estimates on the correlations between Bitcoin and the US stock markets strongly predict lower subsequent Bitcoin returns, consistent with a mean-variance framework. However, portfolio optimization errors associated with uncertainty in volatilities are 30 times greater than those with correlations; therefore, volatility-related predictors fail to explain Bitcoin returns. The same empirical patterns appear in out-of-sample predictions, global equity markets, and other cryptocurrencies.

A model for dynamical solvent control of molecular junction electronic properties

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control the electric current through a molecule. In this paper, we propose a model that includes dynamical effects of solvent-molecule interaction in non-equilibrium Green's function calculations of the electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunneling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in the time domain with subsequent averaging over random realizations of rotational variables using the Furutsu-Novikov method for the exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wideband approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Alignment of the rotating dipole moment breaks the particle-hole symmetry of the transmission favoring either hole or electron transport channels depending upon the aligning potential.

A multivariate 4/2 stochastic covariance model: properties and applications to portfolio decisions

This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in [Grasselli, M., The 4/2 stochastic volatility model: A unified approach for the Heston and the 3/2 model. Math. Finance, 2017, 27(4), 1013–1034]. Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Markowitz Portfolio Selection for Multivariate Affine and Quadratic Volterra Models

This paper concerns portfolio selection with multiple assets under rough covariance matrix. We investigate the continuous-time Markowitz mean-variance problem for a multivariate class of affine and quadratic Volterra models. In this incomplete non-Markovian and nonsemimartingale market framework with unbounded random coefficients, the optimal portfolio strategy is expressed by means of a Riccati backward stochastic differential equation (BSDE). In the case of affine Volterra models, we derive explicit solutions to this BSDE in terms of multidimensional Riccati--Volterra equations. This framework includes multivariate rough Heston models and extends the results of Han and Wong [Appl. Math. Optim. (2020)]. In the quadratic case, we obtain new analytic formulae for the the Riccati BSDE and we establish their link with infinite-dimensional Riccati equations. This covers rough Stein--Stein and Wishart type covariance models. Numerical results on a two-dimensional rough Stein--Stein model illustrate the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategy. In particular for positively correlated assets, we find that the optimal strategy in our model is a “buy rough sell smooth” one.