scholarly journals Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation

2020 ◽  
Author(s):  
László Márkus ◽  
Ashish Kumar
Keyword(s):  
Stock Prices ◽  
Goodness Of Fit ◽  
Tail Dependence ◽  
Heston Model ◽  
Gaussian Copula ◽  
Suitable Model ◽  
Stochastic Correlation ◽  
Wiener Processes ◽  
Correlation Models ◽  
Joint Behaviour

Abstract Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation models, two goodness-of-fit procedures are proposed based on the copula of Wiener increments. One uses the confidence domain for the centered Kendall function, and the other relies on strong and weak tail dependence. The constant correlation model and two different stochastic correlation models, given by Jacobi and hyperbolic tangent transformation of Ornstein-Uhlenbeck (HtanOU) processes, are compared by analyzing daily close prices for Apple and Microsoft stocks. The constant correlation, i.e., the Gaussian copula model, is unanimously rejected by the methods, but all other two are acceptable at a 95% confidence level. The analysis also reveals that even for Wiener processes, stochastic correlation can create tail dependence, unlike constant correlation, which results in multivariate normal distributions and hence zero tail dependence. Hence models with stochastic correlation are suitable to describe more dangerous situations in terms of correlation risk.

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

2021 ◽  
Author(s):  
Gaetano La Bua ◽  
Daniele Marazzina
Keyword(s):  
Mathematical Finance ◽  
Calibration Procedure ◽  
Heston Model ◽  
Stochastic Correlation ◽  
Equity Derivatives ◽  
Single Instance ◽  
Asset Volatility ◽  
Wishart Process ◽  
Definition Of ◽  
Joint Behaviour

AbstractGiven 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.

scholarly journals Joint Modeling of Precipitation and Temperature Using Copula Theory for Current and Future Prediction under Climate Change Scenarios in Arid Lands (Case Study, Kerman Province, Iran)

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
T. Mesbahzadeh ◽  
M. M. Miglietta ◽  
M. Mirakbari ◽  
F. Soleimani Sardoo ◽  
M. Abdolhoseini
Keyword(s):  
Climate Change ◽  
Goodness Of Fit ◽  
Joint Modeling ◽  
Copula Function ◽  
Gaussian Copula ◽  
Climate Change Scenarios ◽  
Climatic Parameters ◽  
Goodness Of Fit Test ◽  
Copula Theory ◽  
Precipitation And Temperature

Precipitation and temperature are very important climatic parameters as their changes may affect life conditions. Therefore, predicting temporal trends of precipitation and temperature is very useful for societal and urban planning. In this research, in order to study the future trends in precipitation and temperature, we have applied scenarios of the fifth assessment report of IPCC. The results suggest that both parameters will be increasing in the studied area (Iran) in future. Since there is interdependence between these two climatic parameters, the independent analysis of the two fields will generate errors in the interpretation of model simulations. Therefore, in this study, copula theory was used for joint modeling of precipitation and temperature under climate change scenarios. By the joint distribution, we can find the structure of interdependence of precipitation and temperature in current and future under climate change conditions, which can assist in the risk assessment of extreme hydrological and meteorological events. Based on the results of goodness of fit test, the Frank copula function was selected for modeling of recorded and constructed data under RCP2.6 scenario and the Gaussian copula function was used for joint modeling of the constructed data under the RCP4.5 and RCP8.5 scenarios.

scholarly journals Tail dependence of the Gaussian copula revisited

2016 ◽  
Vol 69 ◽  
pp. 97-103 ◽  
Author(s):  
Edward Furman ◽  
Alexey Kuznetsov ◽  
Jianxi Su ◽  
Ričardas Zitikis
Keyword(s):  
Tail Dependence ◽  
Gaussian Copula

scholarly journals A Method for Systemic Risk Estimation Based on CDS Indices

2015 ◽  
Vol 8 (1) ◽  
pp. 103-124
Author(s):  
Gabriel Gaiduchevici
Keyword(s):  
Goodness Of Fit ◽  
Risk Estimation ◽  
Multivariate Time Series ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Parameter Estimates ◽  
Copula Models ◽  
Goodness Of Fit Tests ◽  
Multi Stage ◽  
Stage Estimation

AbstractThe copula-GARCH approach provides a flexible and versatile method for modeling multivariate time series. In this study we focus on describing the credit risk dependence pattern between real and financial sectors as it is described by two representative iTraxx indices. Multi-stage estimation is used for parametric ARMA-GARCH-copula models. We derive critical values for the parameter estimates using asymptotic, bootstrap and copula sampling methods. The results obtained indicate a positive symmetric dependence structure with statistically significant tail dependence coefficients. Goodness-of-Fit tests indicate which model provides the best fit to data.

scholarly journals Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability

2020 ◽  
Vol 6 (10) ◽  
pp. 2002-2023
Author(s):  
Shahid Latif ◽  
Firuza Mustafa
Keyword(s):  
Failure Probability ◽  
Goodness Of Fit ◽  
Peak Flow ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Distribution Analysis ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Flood Peak ◽  
Flood Volume

Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF

scholarly journals Dependence in the Banking Sector of the United States and Mexico: A Copula Approach

2021 ◽  
Vol 16 (TNEA) ◽  
pp. 1-23
Author(s):  
Christian Bucio Pacheco ◽  
Luis Villanueva ◽  
Raúl de Jesús Gutiérrez
Keyword(s):  
United States ◽  
Stock Prices ◽  
Banking Sector ◽  
Tail Dependence ◽  
The United States ◽  
Small Sample ◽  
High Dependency ◽  
The Us ◽  
Rolling Windows ◽  
Main Banks

The objective of this work is to estimate the patterns of dependence between the yields of the stock prices of the main banks of the United States (US) and Mexico. We estimate the patterns of absolute dependence and tail dependence through copulas of the Archimedean family and the use of rolling windows of 245 days. The data employed come from the daily share prices at closing from January 2, 2015, to December 31, 2020, for seven banks. Our results show that: i) there are patterns of high dependence among the main banks in the US, ii) there are patterns of very low dependence among the main banks in the US and Mexico, and iii) there are patterns of low dependence among the main banks in Mexico. These results have several implications, among them that the high-dependency patterns obtained among major US banks limit the joint selection of these US bank equity assets in an investment portfolio. Although this paper focuses on a small sample of banks, they represent an important portion of the banking sector in both countries. Given the limited literature on this subject in Mexico, our paper contributes to expanding this literature with a novel approach.

Nonlinear stochastic correlation models for the pole’s motion of a deformable Earth

2003 ◽  
Vol 47 (2) ◽  
pp. 161-167
Author(s):  
Yu. G. Markov ◽  
I. N. Sinitsyn
Keyword(s):  
Stochastic Correlation ◽  
Correlation Models

Stochastic volatility and the goodness-of-fit of the Heston model

2005 ◽  
Vol 5 (2) ◽  
pp. 199-211 ◽  
Author(s):  
Gilles Daniel ◽  
Nathan L. Joseph * ◽  
David S. Brée
Keyword(s):  
Stochastic Volatility ◽  
Goodness Of Fit ◽  
Heston Model

New Metrics for Validation of Data-Driven Random Process Models in Uncertainty Quantification

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Hongyi Xu ◽  
Zhen Jiang ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Experimental Tests ◽  
Process Models ◽  
Data Driven ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Marginal Distributions

Data-driven random process models have become increasingly important for uncertainty quantification (UQ) in science and engineering applications, due to their merit of capturing both the marginal distributions and the correlations of high-dimensional responses. However, the choice of a random process model is neither unique nor straightforward. To quantitatively validate the accuracy of random process UQ models, new metrics are needed to measure their capability in capturing the statistical information of high-dimensional data collected from simulations or experimental tests. In this work, two goodness-of-fit (GOF) metrics, namely, a statistical moment-based metric (SMM) and an M-margin U-pooling metric (MUPM), are proposed for comparing different stochastic models, taking into account their capabilities of capturing the marginal distributions and the correlations in spatial/temporal domains. This work demonstrates the effectiveness of the two proposed metrics by comparing the accuracies of four random process models (Gaussian process (GP), Gaussian copula, Hermite polynomial chaos expansion (PCE), and Karhunen–Loeve (K–L) expansion) in multiple numerical examples and an engineering example of stochastic analysis of microstructural materials properties. In addition to the new metrics, this paper provides insights into the pros and cons of various data-driven random process models in UQ.

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