[4] |
A. Schröter and P. Heider: Numerical Methods to Quantify the Model Risk of Basket Default Swaps. Journal of Computational and Applied Mathematics, Volume 251, Pages 117-132, DOI, 2013.
The valuation of basket default swaps depends crucially on the joint default probability of the underlying assets in the basket.
It is known that this probability can be modeled by means of a copula function which links the marginal default probabilities to a joint probability.
The valuation bears risk due to the uncertainty of the copula, the relation of the assets to each other and the marginal distributions which we call together the model risk.
To value basket default swaps and to compute model risk parameters we present an efficient numerical approach based on importance sampling and applicable to different classes of copula models.
Our numerical findings show that the choice of the underlying copula model influences strongly the risk profile of the basket and should be tailored advisedly.
|
[3] |
A. Schröter and P. Heider: An analytical formula for pricing m-th to default swaps.
Journal of Applied Mathematics and Computing, Volume 41, Issue 1-2, Pages 229-255, DOI, 2013.
The computational effort of pricing an m-th to default swap depends highly on the size n of
the underlying basket. Usually, n different default times are modeled, but in fact the valuation
only depends on the m-th smallest default time of this tuple. In this paper we attain an analytical
formula for the distribution of this m-th default time. With the help of this distribution we simplify
the valuation problem from an n-dimensional integral to an one-dimensional integral and break the
curse of dimensionality. Applications of this modi cation are rapid pricing of m-th to default swaps,
estimation of sensitivities and pricing of European max/min options.
|
[2] |
A. Schröter: A Fast Quadrature Method for Pricing Basket Default Swaps by Means of Copulae.
PhD thesis, URL, Mathematical Institute, University of Cologne, 2012.
The computational effort of pricing an m-th to Default Swap highly depends on the
size d of the underlying basket. Usually, d different default times are modeled, but in
many cases the evaluation only depends on the m-th smallest default time. In this
thesis we develop the distribution function F of the m-th default time by means
of copulae. With the help of this distribution we reduce the dimension of the pricing
problem from d to one and break the curse of dimensionality. In order to ensure
an efficient evaluation of F we apply suitable recursion schemes. Independently
of the chosen copula, the resulting quadrature offers a very fast convergence and a
complexity of at worst O(N^2 d^2) by using N nodes. If the underlying m-th to Default
Swap does not depend on the m-th smallest default time solely, we will develop
new Monte-Carlo methods in this thesis. For this, we extend existing importance
sampling methods regarding the Gaussian copula to the usage of any Archimedean
copula. Besides the pricing of m-th to Default Swaps, other applications of the
presented methods are pricing European max/min options or calculating sensitivities of any kind.
|
German