Sabrina Mulinacci

An approximation of American option prices in a jump-diffusion model

In this paper, an effectively computable approximation of the price of an American option in a jump-diffusion market model will be shown: results of convergence in Lp and a.s. will be proved.

Functional convergence of Snell envelopes: Applications to American options approximations

Abstract. The main result of the paper is a stability theorem for the Snell envelope under convergence in distribution of the underlying processes: more precisely, we prove that if a sequence

A copula-based model of speculative price dynamics in discrete time

(X^n)

Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures

of stochastic processes converges in distribution for the Skorokhod topology to a process

Marshall ̶ Olkin Distributions - Advances in Theory and Applications

X

The efficient hedging problem for American options

and satisfies some additional hypotheses, the sequence of Snell envelopes converges in distribution for the Meyer–Zheng topology to the Snell envelope of

Marshall–Olkin Machinery and Power Mixing: The Mixed Generalized Marshall–Olkin Distribution

X

A Copula-Based Model of the Term Structure of CDO Tranches

(a brief account of this rather neglected topology is given in the appendix). When the Snell envelope of the limit process is continuous, the convergence is in fact in the Skorokhod sense. This result is illustrated by several examples of approximations of the American options prices; we give moreover a kind of robustness of the optimal hedging portfolio for the American put in the Black and Scholes model.

Contagion-based distortion risk measures

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a sequence of copula functions representing dependence between each increment of the process and the corresponding level of the process before the increment. The paper shows how to use the approach to build several kinds of processes (stable, elliptical, Farlie-Gumbel-Morgenstern, Archimedean and martingale processes), and how to extend the analysis to the multivariate setting. The technique turns out to be well suited to provide a discrete time representation of the dynamics of innovations to financial prices under the restrictions imposed by the Efficient Market Hypothesis.

A Copula-Based Model for Spatial and Temporal Dependence of Equity Markets

In this paper we study the dependence properties of a family of bivariate distributions (that we call Archimedean-based Marshall-Olkin distributions) that extends the class of the Generalized Marshall-Olkin distributions of Li and Pellerey, J Multivar Anal, 102, (10), 1399–1409, 2011 in order to allow for an Archimedean type of dependence among the underlying shocks’ arrival times. The associated family of copulas (that we call Archimedean-based Marshall-Olkin copulas) includes several well known copula functions as specific cases for which we provide a different costruction and represents a particular case of implementation of Morillas, Metrika, 61, (2), 169–184, 2005 construction. It is shown that Archimedean-based copulas are obtained through suitable transformations of bivariate Archimedean copulas: this induces asymmetry, and the corresponding Kendall’s function and Kendall’s tau as well as the tail dependence parameters are studied. The type of dependence so modeled is wide and illustrated through examples and the validity of the weak Lack of memory property (characterizing the Marshall-Olkin distribution) is also investigated and the sub-family of distributions satisfying it identified. Moreover, the main theoretical results are extended to the multidimensional version of the considered distributions and estimation issues discussed.