Consider the sum Y=B+B^H of a Brownian motion B and an independent fractional Brownian motion B^H with Hurst parameter H ∈ (0,1). Surprisingly, even though B^H is not a semimartingale, Cheridito proved in that Y is a semimartingale if H3/4. Moreover, Y is locally equivalent to B in this case,...

We suggest three superpositions of COGARCH (sup-CO-GARCH) volatility processes driven by Lévy processes or Lévy bases. We investigate second-order properties, jump behaviour, and prove that they exhibit Pareto-like tails. Corresponding price processes are defined and studied. We find that the...

We develop a structural default model for interconnected financial institutions in a probabilistic framework. For all possible network structures we characterize the joint default distribution of the system using Bayesian network methodologies. Particular emphasis is given to the treatment and...

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an Itô semimartingale over a shrinking time interval. The spot characteristics of the Itô semimartingale are allowed to have dynamics of general form. In particular, their paths can be...

In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H0.5. In this paper,...

Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous...

A new concept of convergence concerning random probability measure is introduced in order to discuss the weak consistency of the bootstrap distribution estimator. Some results on random probabilities and conditional distributions corresponding to the classical theorems are proved. Finally we...

An effective data-analytic tool, sliced inverse regression(SIR), for the analysis of multivariate data was developed by Li (Technical Report, Department of Mathematics, UCLA, 1989) and Duan and Li (J. Amer. Statist. Assoc. 86 (1991) 316). It is a method for dimension reduction. Let (Y,X) be a...