Elliptical families and copulas: tilting and premium; capital allocation

Elliptical copula measures with symmetrical marginals are proposed as a natural generalization of the elliptical family, which preserves the symmetrical character of marginals, but is more flexible in the choice of their shape parameters. The properties of these copulas are investigated and the elliptical copula tilting and corresponding premium are proposed as a natural tool for portfolio capital allocation. For the case of the multivariate normal family, such a tilting and premium coincide with the Esscher transform and premium.     

THE DEPENDENCE STRUCTURE OF RUNNING MAXIMA AND MINIMA: RESULTS AND OPTION PRICING APPLICATIONS

We provide general results for the dependence structure of running maxima (minima) of sets of variables in a model based on (i) Markov dynamics; (ii) no Granger causality; (iii) cross-section dependence. At the time series level, we derive recursive formulas for running minima and maxima. These formulas enable to use a "bootstrapping" technique to recursively recover the pricing kernels of barrier options from those of the corresponding European options. We also show that the dependence formulas for running maxima (minima) are completely defined from the copula function representing dependence among levels at the terminal date. The result is applied to multivariate discrete barrier digital products. Barrier Altiplanos are simply priced by (i) bootstrapping the price of univariate barrier products; (ii) evaluating a European Altiplano with these values.     

Strategic Asset Allocation for China＇s Foreign Reserves： A Copula Approach

In this paper, we study strategic asset allocation for China＇s foreign reserves using a risk- based approach. Four aspects of the risk management are investigated： an investment universe, dependence structure, allocation strategies under risk minimization and trade-off between risks and returns. A regime-switching copula model is developed to investigate the dynamic dependence between assets. One regime emphasizes a short-term safe asset and the other regime emphasizes a long-term safe asset. The optimal allocation is derived following two strategies： risk minimization and trade-off between risks and returns in utility maximization with disappointment avoidance, lf the central bank focuses solely on risk minimization, the asymmetries in the asset return dependence encourage the flight to safety. However, if higher risks are allowed in exchange for higher returns, even the exchange is very conservative, and the asymmetries would discourage the flight to safety. Therefore, we suggest that China should mitigate its flight to safety after 2008 and increase holdings of short-term bank deposits, long-term treasury bonds and euro bonds.     

An Investigation of the Flight-to-Quality Effect: Evidence from Asia-Pacific Countries

Flight to quality has long been a feature of international financial markets when there are extreme variations in the negative relationship between returns on stocks and sovereign bond indices. This study analyzes the existence of a flight-to-quality effect from stocks to long-term government bonds in five Asia-Pacific countries by modeling a dependency structure from a copula-based perspective. The authors employ various copula functions to examine the degrees of dependence on symmetric and asymmetric structures in these countries. They find a negative relationship between stock and bond returns, that there is a flight to quality in the Asia-Pacific region, and that it intensified during the financial crisis period, indicating that investors considered government bonds to be safer financial instruments than stocks during this period. Furthermore, the authors show that the level of economic freedom in a country affects the tendency toward flight to quality.     

Linear and non-linear transmission of equity return volatility: evidence from the US, Japan and Australia

This paper models the transmission of shocks between the US, Japanese and Australian equity markets. Tests for the existence of linear and non-linear transmission of volatility across the markets are performed using parametric and non-parametric techniques. In particular the size and sign of return innovations are important factors in determining the degree of spillovers in volatility. It is found that a multivariate asymmetric GARCH formulation can explain almost all of the non-linear causality between markets. These results have important implications for the construction of models and forecasts of international equity returns.     

Extreme dependence of multivariate catastrophic losses

Natural catastrophes cause insurance losses in several different lines of business. An approach to modelling the dependence in loss severities is to assume that they are related to the intensity of the natural disaster. In this paper we introduce a factor model and investigate the extreme dependence. We derive a specific extreme dependence structure when considering an heavy-tailed intensity. Estimation procedures are presented and their moderate sample properties are compared in a simulation study. We also motivate our approach by an illustrative example from storm insurance.     

BookReview

We compare the bias in binomial trees against that in certain analytical/numerical valuation techniques with which they disagree. We consider the CRR tree, the COS method and the Leisen–Reimer as well as the Prekopa–Szantai exponentially smoothed method. We conclude that the binomial trees are unbiased and that the exponentially smoothed method is biased.     

Prediction of bank financial strength ratings: The case of Turkey

Bank financial strength ratings have gained widespread popularity especially after the recent financial turmoil. Rating agencies were criticized because of their ratings and failure to predict the bankruptcy of the banks. Based on this observation, we investigate whether the forecast of the rating of bank's financial strength using publicly available data is consistent with those of the credit rating agency. We use the data of Turkish banks for this investigation. We take a country-specific approach because previous studies found that proxies used for environmental factors (political, economic, and financial risk of the country) did not have any explanatory power and it is hard to find international data for other important factors such as franchise value, concentration, and efficiency. We use two popular multivariate statistical techniques (multiple discriminant analysis and ordered logistic regression) to estimate a suitable model and we compare their performances with those of two mostly used data mining techniques (Support Vector Machine and Artificial Neural Network). Our results suggest that our predictions are consistent with those of Moody's financial strength rating in general.. The important factors in rating are found to be profitability (measured by return on equity), efficient use of resources, and funding the businesses and the households instead of the government that shows efficient placement of the funds.     

GRAPHICAL MODELS FOR CORRELATED DEFAULTS

A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These techniques also provide a calibration algorithm based on maximum likelihood estimation. Finally, the model is compared with standard normal copula model in terms of tails of the loss distribution and implied correlation smile.     

Measuring large comovements in financial markets

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.