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Browsing Publications by Subject "copulas"

Now showing 1 - 4 of 4
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    A copula-based approach for generating lattices
    (Colorado State University. Libraries, 2015-07-02) Wang, Tianyang, author; Dyer, James S., author; Hahn, Warren J., author; Review of Derivatives Research, publisher
    Discrete approximations such as binomial and trinomial lattices have been developed to model the intertemporal dynamics of variables in a way that also allows contingent decisions to be included at the appropriate increments in time. In this paper we present an approach for developing these types of models based on copulas. In addition to ease of implementation, a primary benefit of this approach is its generality, and we show that various binomial and trinomial approximation methods for valuing contingent claim securities in the literature are special cases of this approach, each based on a choice of a particular set of probability and/or branching parameters. Because this approach encompasses these and other cases as feasible solutions, we also show how it can be used to optimize the construction of lattices so that discretization error is minimized, and we demonstrate its application for an option pricing example.
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    A copulas-based approach to modeling dependence in decision trees
    (Colorado State University. Libraries, 2012-01) Wang, Tianyang, author; Dyer, James, author; Operations Research, publisher
    This paper presents a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree. The proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions. This general framework could be naturally applied in decision analysis and real options valuations, as well as in more general applications of dependent probability trees. While this approach to modeling dependencies can be based on several popular copula families as we illustrate, we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application.
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    Modeling correlated discrete uncertainties in event trees with copulas
    (Colorado State University. Libraries, 2015-07-14) Wang, Tianyang, author; Dyer, James S., author; Butler, John C., author; Risk Analysis, publisher
    Modeling the dependence between uncertainties in decision and risk analyses is an important part of the problem structuring process. We focus on situations where correlated uncertainties are discrete, and extend the concept of the copula‐based approach for modeling correlated continuous uncertainties to the representation of correlated discrete uncertainties. This approach reduces the required number of probability assessments significantly compared to approaches requiring direct estimates of conditional probabilities. It also allows the use of multiple dependence measures, including product moment correlation, rank order correlation and tail dependence, and parametric families of copulas such as normal copulas, t‐copulas, and Archimedean copulas. This approach can be extended to model the dependence between discrete and continuous uncertainties in the same event tree.
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    Sensitivity analysis of decision making under dependent uncertainties using copulas
    (Colorado State University. Libraries, 2017-10-03) Wang, Tianyang, author; Dyer, James S., author; Hahn, Warren J., author; EURO Journal on Decision Processes, publisher
    Many important decision and risk analysis problems are complicated by dependencies between input variables. In such cases, standard one-variable-at-a-time sensitivity analysis methods are typically eschewed in favor of fully probabilistic, or n-way, analysis techniques which simultaneously vary all n input variables and capture their interdependencies. Unfortunately, much of the intuition provided by one-way sensitivity analysis may not be available in fully probabilistic methods because it is difficult or impossible to isolate the marginal effects of the individual variables. In this paper, we present a dependence-adjusted approach for identifying and analyzing the impact of the input variables in a model through the use of probabilistic sensitivity analysis based on copulas. This approach provides insights about the influence of the input variables and the dependence relationships between the input variables. One contribution of this approach is that it facilitates assessment of the relative marginal influence of variables for the purpose of determining which variables should be modeled in applications where computational efficiency is a concern, such as in decision tree analysis of large scale problems. In addition, we also investigate the sensitivity of a model to the magnitude of correlations in the inputs.