Discussion Papers represent the authors' personal opinions and do not necessarily reflect the views of the Deutsche Bundesbank or its staff. Abstract The credit value-at-risk model underpinning the Basel II Internal Ratings-Based approach assumes that idiosyncratic risk has been diversified away fully in the portfolio, so that economic capital depends only… (More)
In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional Itô-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently regular density. In this article we first prove results on absolute… (More)
In this paper we determine the lowest cost strategy for a given payoff in Lévy markets where the pricing is based on the Esscher mar-tingale measure. In particular, we consider Lévy models where the price process is driven by an NIG-and a VG-process. Explicit solutions for cost-efficient strategies are derived for a variety of vanilla options, spreads, and… (More)
In this paper we derive explicit representations for cost-efficient puts and calls in financial markets which are driven by a Lévy process and where the pricing of derivatives is based on the Esscher martingale measure. Whereas the construction and evaluation of the efficient self-quanto call is a straightforward application of the general theory, the… (More)
and by the Excellence Initiative through the project " Pricing of Risk in Incomplete Markets " within the Institutional Strategy of the University of Freiburg. The financial support is gratefully acknowledged by the first and the second authors. Several helpful comments and suggestions from Lishang Jiang, Yajun Xiao, and Qianzi Zeng are very much… (More)
A perturbation involving a small parameter of the Black-Scholes-Merton model with time dependent volatility is considered. A pricing formula is derived as an asymptotic series in powers of the small parameter. The summation of this series is performed, using methods of the theory of Borel summability in a suitable direction.