We explore the class of second-order weak approximation schemes (cubature methods) for the numerical simulation of joint default probabilities in credit portfolios where the firm's asset value processes are assumed to follow the multivariate Heston stochastic volatility model. Correlation...

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 prices are driven by a normal inverse Gaussian (NIG)- or a variance Gamma (VG)-process. Explicit...

Within the Internal Ratings-Based (IRB) approach of Basel II it is assumed that idiosyncratic risk has been fully diversi?ed away. The impact of undiversi?ed idiosyncratic risk on portfolio Value-at-Risk can be quanti?ed via a granularity adjustment (GA). We provide an analytic formula for the...

We show that the saddle-point approximation method to quantify the impact of undiversi?ed idiosyncratic risk in a credit portfolio is inappropriate in the presence of double default effects. Speci?cally, we prove that there does not exist an equivalent formula to the granularity adjustment, that...

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...

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...

A firm-value model similar to the one proposed by Black and Cox (1976) is considered. Instead of assuming a constant and known default boundary, the default boundary is an unobserved stochastic process. This process has a Brownian component, reflecting the influence of uncertain effects on the...

The defaultable term structure is modeled using stochastic differential equations in Hilbert spaces. This leads to an infinite dimensional model, which is free of arbitrage under a certain drift condition. Furthermore, the model is extended to incorporate ratings based on a Markov chain.

In this article we propose and study a model for stock prices which allows for shot-noise effects. This means that abrupt changes caused by jumps may fade away as time goes by. This model is incomplete. We derive the minimal martingale measure in discrete and continuous time and discuss the...

The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a unified view on both approaches. This is achieved by...