Dynamic Copula Processes (original) (raw)

Multivariate Option Pricing Using Dynamic Copula Models

SSRN Electronic Journal, 2000

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets. Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets. These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes. Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels. Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.

Copula-based dynamic models for multivariate time series

Journal of Multivariate Analysis

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Dynamic Modeling of Dependence in Finance via Copulae Between Stochastic Processes

Lecture Notes in Statistics, 2010

Modeling of stochastic dependence is crucial to pricing and hedging of basket derivatives, as well as to pricing and hedging of some other financial products, such as rating-triggered corporate step-up bonds. The classical approach to modeling of dependence in finance via static copulae (and Sklar's theorem) is inadequate for consistent valuation and hedging in time. In this survey we present recent developments in the area of modeling of dependence between stochastic processes with given marginal laws. Some of these results have already been successfully applied in finance in connection with the portfolio credit risk.

Efficient Bayesian inference for stochastic time-varying copula models

Computational Statistics & Data Analysis, 2012

There is strong empirical evidence that dependence in multivariate financial time series varies over time. To incorporate this effect we suggest a time varying copula class, which allows for stochastic autoregressive (SCAR) copula time dependence. For this we introduce latent variables which are analytically related to Kendall's τ , specifically we introduce latent variables that are the Fisher transformation of Kendall's τ allowing for easy comparison of different copula families such as the Gaussian, Clayton and Gumbel copula. The inclusion of latent variables renders maximum likelihood estimation computationally infeasible, therefore a Bayesian approach is followed. Such an approach also enables credibility intervals to be easily computed in addition to point estimates. We design two sampling approaches in a Markov Chain Monte Carlo (MCMC) framework. The first is a naïve approach based on Metropolis-Hastings in Gibbs while the second is a more efficient coarse grid sampler using ideas of Liu and Sabatti (2000). The performance of these samplers are investigated in a large simulation study and are applied to two data sets involving financial stock indices. It is shown that time varying dependence is present for these data sets and can be quantified by estimating time varying Kendall's τ with point-wise credible intervals over the series.

Multivariate Dynamic Copula Models: Parameter Estimation and Forecast Evolution

SSRN Electronic Journal, 2000

This paper introduces multivariate dynamic copula models to account for the timevarying dependence structure in asset portfolios. We firstly enhance the flexibility of this structure by modeling regimes with multivariate mixture copulas. In our second approach, we derive dynamic elliptical copulas by applying the dynamic conditional correlation model (DCC) to multivariate elliptical copulas. The best-ranked copulas according to both in-sample fit and out-of-sample forecast performance indicate the importance of accounting for time-variation. The superiority of multivariate dynamic Clayton and Student-t models further highlight that tail dependence as well as the capability of capturing asymmetries in the dependence structure are crucial features of a well-fitting model for an equity portfolio.

Some Statistical Pitfalls in Copula Modeling for Financial Applications

Social Science Research Network, 2004

In this paper we discuss some statistical pitfalls that may occur in modeling cross-dependences with copulas in financial applications. In particular we focus on issues arising in the estimation and the empirical choice of copulas as well as in the design of time-dependent copulas.

Inhomogeneous dependence modeling with time-varying copulae

2009

Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of applications, though, requires a modelling framework different from the multivariate normal. In risk management the non-normal behaviour of most financial time series calls for non-gaussian dependency. The correct modelling of non-gaussian dependencies is therefore a key issue in the analysis of multivariate time series. In this paper we use copulae functions with adaptively estimated time varying parameters for modelling the distribution of returns, free from the usual normality assumptions. Further, we apply copulae to estimation of Valueat-Risk (VaR) of a portfolio and show its better performance over the RiskMetrics approach, a widely used methodology for VaR estimation.