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Part I
Financial Econometrics and International Finance
The financial econometrics section in this book includes five chapters that cover topics in interest rate modeling, portfolio allocation, risk management and credit risk. The first two chapters deal with modeling multivariate interest-rate processes using time-varying copula functions that allow for dynamic and complex dependence among financial series. The third chapter studies intertemporal portfolio allocation under a time-varying covariance matrix of stock returns using a dynamic conditional correlation model. The fourth chapter is on portfolio risk management using a copula-based model that accounts for the distributional characteristics and tail dependence of stock returns. The fifth chapter focuses on credit risk analysis using an option-based approach and nonlinear filtering techniques that allow for jump-diffusions in the underlying asset price. These analytical methods are applied to data from both developed and emerging financial markets.
In their chapter entitled âModeling Interest Rates Using Reducible Stochastic Differential Equations: A Copula-base Multivariate Approach,â Ruijun Bu, Ludovic Giet, Kaddour Hadri and Michel Lubrano consider a class of nonlinear stochastic differential equations for modeling the marginal processes of interest rates that are reducible to generalized versions of a mean-reversion process with time-varying volatility. This approach can account for nonlinear features observed in short-term interest-rate series and lead to exact discretization and closed-form likelihood functions. Results from an application to the UK and US interest-rate data suggest that the proposed generalized models outperform existing parametric models with closed-from likelihood functions. The authors also study the dynamic co-movements between the two rates using the conditional symmetrized JoeâClayton copula and find that the time-varying effects as well as the asymmetry in the tail dependence implied by the copula are significant. There is evidence that the level of dependence is positively related to the level of the two rates.
In the chapter entitled âTime-varying Dependence in the Term Structure of Interest Rates: A Copula-based Approach,â Diaa Noureldin investigates the dependence structure of the level, slope and curvature factors for the US yield curve. The author extends the dynamic version of the NelsonâSiegel model for estimating these three latent factors that drive yields at different maturities by allowing for time-varying dependence among them. The analysis of the correlated factor dynamics using conditional elliptical copulas indicates that there is evidence of time-varying dependence structure among the factors. The time variation in factor dynamics is largely explained by past shocks and characterized by low persistence. Also, simulation results indicate that an invalid assumption of constant dependence among the yield curve factors leads to serious errors in risk assessment for bond portfolios.
In the chapter entitled âTime-varying Optimal Weights for International Asset Allocation in African, and South Asian Markets,â Dalia El-Edel presents an intertemporal analysis of asset allocation for internationally diversified portfolios from the perspective of domestic investors in selected emerging markets. The time-varying optimal portfolio weights are computed from a dynamic conditional correlation model. Estimation results of the model indicate that the share of domestic equities is generally small in the optimal portfolios. Also, there is increasing correlation between stock indices of emerging markets during crisis times.
In the chapter entitled âFinancial Risk Management Using Asymmetric Heavy-tailed Distributions and Nonlinear Dependence Structures of Asset Returns under Discontinuous Dynamics,â Alaa El-Shazly studies a copula-based model for portfolio risk management when asset price dynamics are driven by non-Gaussian Levy processes. The model uses the Normal Inverse Gaussian distribution and the t-copula function to account for the distributional characteristics and tail dependence of asset returns. The modeling scheme allows measuring the strength of nonlinear relationships among the portfolio components under both normal and extreme market conditions. Application to data from developed and emerging stock markets suggests that the model yields useful information on dependence structure of the return distributions for devising portfolio and risk management strategies with a reasonably good predictive power based on conditional value-at-risk estimation.
In the chapter entitled âNonlinear Filtering and Market Implied Rating for a Jump-diffusion Structural Model of Credit Risk,â Alaa El-Shazly puts forward an asset-based model for credit risk analysis in the context of a nonlinear and non-Gaussian state-space system to compute default probability and related metrics under realistic market conditions. The model draws on option pricing theory and allows for jump-diffusions in the underlying asset value. The author uses particle filtering for online estimation of latent state and parameters to assess credit risk and imply rating from market data as they arrive. Results from a simulation study show good performance of the information filtering method.
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Chapter 1
Modeling Interest Rates Using Reducible Stochastic Differential Equations: A Copula-based Multivariate Approach
Ruijun Bu
University of Liverpool, UK
Ludovic Giet
GREQAM (Groupe de Recherche en economie quantitative dâaix Marseille), France
Kaddour Hadri
Queenâs University Belfast, UK
Michel Lubrano
GREQAM (Groupe de Recherche en economie quantitative dâaix Marseille) and CNRS (Centre National de la Recherche scientifique)
1. Introduction
Continuous-time models have proved to be enormously useful in modeling financial and more generally economic variables. They are widely used to study issues that include the decision to optimally consume, save and invest, portfolio choice under a variety of constraints, contingent claim pricing, capital accumulation, resource extraction, game theory, and recently contract theory. The short-term risk-free interest rate is one of the key variables in economics and finance. More models have been put forward to explain its behavior than for any other issue in finance (Chan et al., 1992). Although many refinements and extensions are possible, the basic continuous-time dynamic model for an interest rate process {rt, t â„ 0} is described by a stochastic differential equation (SDE):
where {Wt, t â„ 0} is a standard Brownian motion. Both parametric and non-parametric methods of estimation have been developed in the literature. Parametric approaches assume that the drift and diffusion are known functions except for an unknown parameter vector. Examples include Merton (1973), Cox (1975), Vasicek (1977), Cox et al. (1980, 1985), Courtadon (1982), Constantinid...
