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In this work we propose a new and general approach to build dependence in multivariate Lévy processes. We fully characterize a multivariate Lévy process whose margins are able to approximate any Lévy type. Dependence is generated by one or more common sources of jump intensity separately in jumps of any sign and size and a parsimonious method to determine the intensities of these common factors is proposed. Such a new approach allows the calibration of any smooth transition between independence and a large amount of linear dependence and provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is analytically tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an accurate multivariate fit of stock returns in terms of linear and nonlinear dependence. A numerical illustration of multi-asset option pricing emphasizes the importance of the proposed new approach for modeling dependence. [ABSTRACT FROM PUBLISHER]

A realistic ARCH process is set up so as to duplicate, for all practical purposes, the properties of stock time series from 1 day to 1 year. The process includes heteroskedasticity with long memory, leverage, fat-tail innovations, relative return, price granularity, and holidays. Its adequacy to describe empirical data is controlled over a broad panel of statistics, including (robust L-statistics) skew, (robust) kurtosis, shape factor for the volatility distribution, and lagged correlations between combinations of return and volatility. These statistics are computed for returns and volatilities with characteristic time intervals ranging from 1 day to 1 year. This wide cross-check between stock time series and simulations ensures that the most important features of the data are correctly captured by the process up to 1 year. The by-products of the statistical analyses and estimations are (1) a positive skew, (2) a cross-sectional relation between kurtosis and heteroskedasticity, (3) a very similar cross-sectional distribution for the statistics evaluated over the empirical data set or for the process with one set of parameters and (4) the heteroskedasticity is very close to an integrated volatility process. [ABSTRACT FROM AUTHOR]

The canonical process used to describe financial time series is based on a logarithmic random walk. Adding a fat-tail distribution for the innovations in this framework creates fundamental inconsistencies, essentially related to a diverging integral. The problems are related to (1) the (infinite) values of statistical quantities for processes with fat-tail innovations, (2) the robustness of computations when dealing with large events (genuine or noise), and (3) the pricing of options with heteroskedasticity and fat tails. Instead of logarithmic processes, we advocate using geometric processes and relative returns so that these problems do not occur. The mathematical properties of geometric processes are explored for setups of increasing complexity. For empirical time series and for processes, the skews are evaluated using a robust estimator and are compared for both return definitions. Finally, the European option pricing framework is modified to use geometric processes for the underlying, allowing the incorporation of natural fat-tail innovations. [ABSTRACT FROM AUTHOR]

This paper contributes to the characterization of the probability density of the price returns in some European day-ahead electricity markets (NordPool, APX, Powernext) by fitting flexible and general families of distributions, such as the α-stable, Normal Inverse Gaussian (NIG), Exponential Power (EP), and Asymmetric Exponential Power (AEP) distributions, and comparing their goodness of fit. The α-stable and the NIG systematically outperform the EP and AEP models, but the tail behavior and the skewness are sensitive to the definition of the returns and to the deseasonalization methods. In particular, the logarithmic transform and volatility rescaling tend to dampen the extreme returns. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool for measuring and controlling the market risk of an asset or portfolio, and is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily understood measure of risk. The use of Product Partition Models allows us to remain in a Normal setting even in the presence of outlying points, and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. The obtained Value-at-Risk estimates are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points. [ABSTRACT FROM AUTHOR]

The need for an accurate representation of tail risk has become increasingly acute in the wake of the credit crisis. We introduce a hyper-cuboid normal mixture copula that permits the representation of complex tail-dependence structures in a multi-dimensional setting. We outline an efficient pattern-recognition calibration methodology that can identify tail dependencies independent of the number of risk factors considered. This model is used to develop a new framework for pricing credit derivative instruments, and we derive semi-analytical and analytical pricing formulae for a first-to-default swap and illustrate with an example valuation. Model assumptions are validated against iTraxx Series 5 equity data over an 8-year period. Identification and representation of tail dependencies is crucial to further the study of contagion dynamics, and our model provides a basis for future research in this area. [ABSTRACT FROM AUTHOR]

The Basel II framework allows the calculation of the capital requirements for market risk with Value-at-Risk models. Since no special model is prescribed in the framework, banks may use simple models with questionable assumptions concerning their underlying distributions. Our numerical analysis reveals that simple VaR models that perform noticeably worse than comparable simple models with more realistic assumptions may lead to a lower level of regulatory capital for banks. For this reason, banks have a major incentive to implement bad models. This is obviously contrary to the interests of regulatory authorities. [ABSTRACT FROM AUTHOR]

The quality of operational risk data sets suffers from missing or contaminated data points. This may lead to implausible characteristics of the estimates. Outliers, especially, can make a modeler's task difficult and can result in arbitrarily large capital charges. Robust statistics provides ways to deal with these problems as well as measures for the reliability of estimators. We show that using maximum likelihood estimation can be misleading and unreliable assuming typical operational risk severity distributions. The robustness of the estimators for the Generalized Pareto distribution, and the Weibull and Lognormal distributions is measured considering both global and local reliability, which are represented by the breakdown point and the influence function of the estimate. [ABSTRACT FROM AUTHOR]

In this paper, we develop a multivariate risk-neutral Levy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Levy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Levy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures. [ABSTRACT FROM AUTHOR]

The present paper studies the non-parametric estimation of volatility in financial time series. Support Vector Regression (SVR) is applied and compared with alternative techniques for estimating a Conditional Heteroskedastic AutoRegressive Nonlinear (CHARN) model. A multiscale decomposition analysis decomposes a time series into several scales, and then several separated SVRs, equal to the number of scales, are fed for running the CHARN model by scaled decomposed series. A multiscale CHARN model, which is an incorporation of wavelet decomposition analysis with a CHARN model estimated by SVR, is proposed and investigated using real-world data sets. To exploit the locality advantage of wavelets, we use wavelet analysis and combine it with SVR. Wavelets are able to economically describe phenomena that are heterogeneous. Recent studies on heterogeneous agents in financial markets theoretically support advocated scale-based analysis of markets, and, of course, the multiscale CHARN model proposition, since it is believed that each scale corresponds to each heterogeneous agent who acts differently in the market. Our objective is to improve the accuracy of estimation by applying multiscale decomposition. The results of applying SVR to estimate the CHARN model in a single resolution on real-world time series indicate that it outperforms the technical benchmarks. Also, the multiscale CHARN model estimated by SVR is more accurate than a single scale model. [ABSTRACT FROM AUTHOR]