Multivariate Option Pricing Using Dynamic Copula Models

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets.Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets.These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes.Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels.Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.option pricing;dynamic models;options

Logistic and Multiple Regression: The Two-Step Approach to Estimating Cost Growth

This study sought to predict cost growth in major Department of Defense (DoD) acquisition programs using logistic and multiple regression. In recent years, the use of statistical regression has proven to be successful in predicting the relationships associated with cost growth. This research follows on the work of Sipple (2002) and Bielecki (2003) and further explores the possibilities of using statistical regression to accurately estimate the dollar value associated with risk and uncertainty early in a program\u27s life cycle. In doing so, the author intends to reduce cost growth by increasing the accuracy of the original cost estimates subsequently used to compute cost growth. The author first used logistic regression to determine whether or not cost growth would occur in a program and, if so, continued with multiple regression to determine to what extent it would occur. Data were compiled from all DoD departments using the Selected Acquisition Reports published between 1990 and 2002. The study analyzes programs during the Engineering and Manufacturing Development phase in the Research and Development, Test and Evaluation (RDT&E) phase of acquisition. For the logistic regression portion of the research, the author produced a seven-variable model that accurately predicted 72 percent of the randomly selected validation data. For multiple regression, a six-variable model was produced that accurately predicted the amount of cost growth incurred for 91 percent of the programs that incurred cost growth. Results show that the two-step regression methodology offers a significant advantage over traditional methods by removing the data points that do not incur cost growth. The author concludes that there is no significant advantage gained by either isolating each cost variance category individually or combining them

A multinomial quadrivariate D-vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable subjects

Diagnostic test accuracy studies observe the result of a gold standard procedure that defines the presence or absence of a disease and the result of a diagnostic test. They typically report the number of true positives, false positives, true negatives and false negatives. However, diagnostic test outcomes can also be either non-evaluable positives or non-evaluable negatives. We propose a novel model for the meta-analysis of diagnostic studies in the presence of non-evaluable outcomes, which assumes independent multinomial distributions for the true and non-evaluable positives, and, the true and non-evaluable negatives, conditional on the latent sensitivity, specificity, probability of non-evaluable positives and probability of non-evaluable negatives in each study. For the random effects distribution of the latent proportions, we employ a drawable vine copula that can successively model the dependence in the joint tails. Our methodology is demonstrated with an extensive simulation study and applied to data from diagnostic accuracy studies of coronary computed tomography angiography for the detection of coronary artery disease. The comparison of our method with the existing approaches yields findings in the real data application that change the current conclusions

Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems

The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound $B$, a PDL formula $\varphi$ and a CFM $\mathcal{C}$, whether every existentially $B$-bounded MSC $M$ accepted by $\mathcal{C}$ satisfies $\varphi$. Recently, it was shown that this problem is PSPACE-complete. In the present work, we consider CRPDL over MSCs which is PDL equipped with the operators converse and repeat. The former enables one to walk back and forth within an MSC using a single path expression whereas the latter allows to express that a path expression can be repeated infinitely often. To solve the model checking problem for this logic, we define message sequence chart automata (MSCAs) which are multi-way alternating parity automata walking on MSCs. By exploiting a new concept called concatenation states, we are able to inductively construct, for every CRPDL formula $\varphi$, an MSCA precisely accepting the set of models of $\varphi$. As a result, we obtain that the model checking problem for CRPDL and CFMs is still in PSPACE

A Graphical Language to Query Conceptual Graphs

This paper presents a general query language for conceptual graphs. First, we introduce kernel query graphs. A kernel query graph can be used to express an "or" between two sub-graphs, or an "option" on an optional sub-graph. Second, we propose a way to express two kinds of queries (ask and select) using kernel query graphs. Third, the answers of queries are computed by an operation based on graph homomorphism: the projection from a kernel query graph