240 research outputs found
Perturbed Copula: Introducing the skew effect in the co-dependence
Gaussian copulas are widely used in the industry to correlate two random
variables when there is no prior knowledge about the co-dependence between
them. The perturbed Gaussian copula approach allows introducing the skew
information of both random variables into the co-dependence structure. The
analytical expression of this copula is derived through an asymptotic expansion
under the assumption of a common fast mean reverting stochastic volatility
factor. This paper applies this new perturbed copula to the valuation of
derivative products; in particular FX quanto options to a third currency. A
calibration procedure to fit the skew of both underlying securities is
presented. The action of the perturbed copula is interpreted compared to the
Gaussian copula. A real worked example is carried out comparing both copulas
and a local volatility model with constant correlation for varying maturities,
correlations and skew configurations.Comment: 34 pages, 6 figures and 3 table
The first passage event for sums of dependent L\'evy processes with applications to insurance risk
For the sum process of a bivariate L\'evy process
with possibly dependent components, we derive a quintuple law describing the
first upwards passage event of over a fixed barrier, caused by a jump, by
the joint distribution of five quantities: the time relative to the time of the
previous maximum, the time of the previous maximum, the overshoot, the
undershoot and the undershoot of the previous maximum. The dependence between
the jumps of and is modeled by a L\'evy copula. We calculate these
quantities for some examples, where we pay particular attention to the
influence of the dependence structure. We apply our findings to the ruin event
of an insurance risk process.Comment: Published in at http://dx.doi.org/10.1214/09-AAP601 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The weighted cross-shareholding complex network: a copula approach to concentration and control in financial markets
In this work, we focus on the cross-shareholding structure in financial markets. Specifically, we build ad hoc indices of concentration and control by employing a complex network approach with a weighted adjacency matrix. To describe their left and right tail dependence properties, we explore the theoretical dependence structure between such indices through copula functions. The theoretical framework has been tested over a high-quality dataset based on the Italian Stock Market. In doing so, we clearly illustrate how the methodological setting works and derive financial insights. In particular, we advance calibration exercises on parametric copulas under the minimization of both Euclidean distance and entropy measure
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