Abstract It is standard in quantitative risk management to model a random vector ${\mathbf {X}:=\lbrace X_{t_k}\rbrace _{k=1,\ldots ,d}}$ of consecutive log-returns to ultimately analyze the probability law of the accumulated return ${X_{t_1}+\cdots +X_{t_d}}$ . By the Markov regression...

Abstract We present a list of challenges one faces when given the task of modeling dependence between stochastic objects, with a special focus on financial applications. Our aim is to draw the readers' attention to common (and not so common) pitfalls and fallacies, and we particularly address...

We present a unification of the Archimedean and the Lévy-frailty copula model for portfolio default models. The new default model exhibits a copula known as scale mixture of Marshall-Olkin copulas and an investigation of the dependence structure reveals that desirable properties of both...

Imposing a symmetry condition on returns, Carr and Lee (Math Financ 19(4):523–560, <CitationRef CitationID="CR10">2009</CitationRef>) show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in...</citationref>

We present a new portfolio default model based on a conditionally independent and identically distributed (CIID) structure of the default times. It combines an intensity-based ansatz in the spirit of Duffie and Gârleanu (2001). Risk and valuation of collateralized debt obligations. <italic>Financial...</italic>

We investigate the calibration of a non-linear pricing model to quoted bid-ask prices and show the existence of a solution in a broad class of distortion risk measures, following the frameworks of Cherny and Madan [<italic>Int. J. Theor. Appl. Financ.</italic>, 2010, <bold>13</bold>(8), 1149-1177] and Bannör and Scherer...</italic>

Two stochastic representations of multivariate geometric distributions are analyzed, both are obtained by lifting the lack-of-memory (LM) property of the univariate geometric law to the multivariate case. On the one hand, the narrow-sense multivariate geometric law can be considered a discrete...

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black–Scholes...

A stochastic time-change is applied to introduce dependence to a portfolio of credit-risky assets whose default times are modeled as random variables with arbitrary distribution. The dependence structure of the vector of default times is completely separated from its marginal default...

A parametric family of n-dimensional extreme-value copulas of Marshall-Olkin type is introduced. Members of this class arise as survival copulas in Lévy-frailty models. The underlying probabilistic construction introduces dependence to initially independent exponential random variables by means...