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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 on systematic risk contributions. We develop a simple methodology for approximating the effect of undiversified idiosyncratic risk on VaR. The… (More)

- Ernst August von Hammerstein, Eva Lütkebohmert, Ludger Rüschendorf, Viktor Wolf
- 2013

In this paper we determine the lowest cost strategy for a given payoff in Lévy markets where the pricing is based on the Esscher martingale measure. In particular, we consider Lévy models where the price process is driven by an NIGand a VG-process. Explicit solutions for cost-efficient strategies are derived for a variety of vanilla options, spreads, and… (More)

- Barbara Forster, Eva Lütkebohmert, Josef Teichmann
- SIAM J. Math. Analysis
- 2008

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)

We show that the saddle-point approximation method to quantify the impact of undiversified idiosyncratic risk in a credit portfolio is inappropriate in the presence of double default effects. Specifically, we prove that there does not exist an equivalent formula to the granularity adjustment, that accounts for guarantees, in case of the extended… (More)

In 2005 the Internal Ratings Based (IRB) approach of ‘Basel II’ was enhanced by a ‘treatment of double default effects’ to account for credit risk mitigation techniques such as ordinary guarantees or credit derivatives. This paper reveals several severe problems of this approach and presents a new method to account for double default effects. This new asset… (More)

We propose a unified structural credit risk model incorporating insolvency, recovery and rollover risks. The firm finances itself mainly by issuing shortand long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. We show that a unique threshold strategy (i.e., a bank run barrier) exists for short-term… (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 selfquanto call is a straightforward application of the general theory, the… (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.

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