Abstract: A system and method for estimating portfolio risk using an infinitely divisible distribution is provided. A time series comprising a plurality of risk factors applicable over at least one time horizon, a portfolio comprising a plurality of financial assets, and one or more risk adjusted return points for the financial assets are stored. The financial assets are associated with the risk factors. The parameters of one or more risk factors such as financial returns series are estimated based on an infinitely divisible tempered stable distribution model exhibiting leptokurtic behavior. Scenarios are generated for the model. One of Value at Risk, Average Value at Risk, and their derivatives are then determined.

Abstract: A system and computer-implemented method for generating random vectors for estimating portfolio risk is provided. Historical financial variable data of financial assets is stored in a memory. Parameters of a copula are estimated. Random vectors are generated from the copula. Risk for the financial assets is calculated based on the random vectors.

Abstract: A system and method for providing reallocation and reverse optimization of a financial portfolio using a parametric leptokurtic distribution are provided. A time series including risk factors applicable over at least one time horizon, a portfolio including financial assets, a quantile, and one or more risk adjusted return points for the financial assets is stored. The financial assets are associated with the risk factors. A subordinated parametric distribution model exhibiting leptokurtic behavior is generated. A function of expected tail loss for the quantile based on the subordinated parametric distribution model exhibiting leptokurtic behavior is expressed. A set of portfolio asset weight changes for each of the financial assets is determined based on the expected tail loss at each such time horizon and for each risk adjusted return point. Reallocation of the portfolio is provided based on the portfolio asset weight changes for each risk adjusted return point for the portfolio.

Abstract: A risk management system and method of determining risk characteristics of portfolios by generating risk factor scenarios based on stable Paretian distributions is provided. The system includes a database for storing any needed input, output, and intermediate results data. At least one module from each of the predefined types can be employed to produce a corresponding result—either intermediate or final. The risk management system and method provide possibilities to use flexible multivariate distribution exhibiting heavy-tails, skewness and different dependence structure, and characterizing the whole distribution of a given financial variable, allows users to perform flexible stress tests on all calculation levels, supplies fast analysis due to the possibility to use intermediate results in many subsequent calculations and to employ several calculation modules in parallel, allows for an efficient enterprise-wide risk management because of the possibility intermediate results to be used by many users.

Abstract: A system and method for providing optimization of a financial portfolio using a parametric leptokurtic distribution is presented. One or more risk factors associated with a plurality of financial assets maintained in a portfolio and applicable over at least one time horizon are provided. A subordinated parametric distribution model having leptokurtic behaviors is specified for the risk factors with a measurement of risk expressed as a function of expected tail loss for a significance level or quantile. The subordinated distribution model is applied at each such time horizon to determine a distribution of the risk factors for the financial assets. Portfolio weights providing a substantially maximum risk adjusted return for the portfolio are determined.

Abstract: A system and method for pricing of derivatives is presented. A volatility clustering time series process, including one or more predictive variables, is generated with an innovation process. Marginals of a probability distribution for the time series process follow a smoothly truncated heavy tailed and asymmetric probability distribution. Model parameters for the time series process are calibrated to a set of exogenously provided derivative prices. Pricing of derivatives, including options and swaps, is determined.