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Modelling Credit Derivatives
PhD Thesis, October 2008
Abstract
PhD thesis on modelling credit correlation derivatives, mainly synthetic CDOs.
Defended on October 24, 2008 at Erasmus University Rotterdam.
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An Implied Loss Model
Working Paper, May 2006
Abstract
In this paper we present a model which is, by construction, consistent with observed market
quotes for standard CDO tranches. The model is closely related to implied tree methods which
can be used for valuing exotic equity derivatives consistent with observed market quotes for
vanilla European call and put options. Rather than modelling default events for each name
in the basket, the total basket loss is modelled directly and calibrated to CDO prices by
construction.
The proposed model has multiple important uses. First, the model can be used as a
tool for avoiding arbitrage opportunities when pricing standard CDO tranches. This is a
problem which is hard to solve when using the market standard Base Correlation approach
in combination with interpolation and extrapolation rules. As a result the proposed model
can be used to determine an arbitrage free distribution for portfolio losses for all maturities,
which can subsequently be used as input to the more complex HJM type models which have
recently become popular. Second, it provides us with a straightforward method for valuing
Forward Starting CDOs, FDOs, consistently with observed market quotes on CDO tranches.
A number of tests have been performed which have shown that the model performs well
for pricing FDOs, when compared to a number of different factor copula models. Moreover,
even under the assumption of heterogeneity of the basket in terms of recovery rates, the
performance of the model is still impressive.
Apart from performance tests, some additional tests have been presented in this paper,
which show that the limited amount of market data still leads to a large amount of uncertainty
in FDO prices.
Finally forward Base Correlation skews implied by the model are considered and these are
found to be rather stable.
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Factor Copulas: Totally External Defaults
Working Paper, April 2005
Abstract
In this paper we address a fundamental problem of the standard one
factor Gaussian Copula model. Within this standard framework a
default event will have a large impact on the default probability
of the survivors, through a shock in available information on the
common factor. Moreover this effect is larger for defaults
occurring instantaneously. In this paper it is shown that this
problem is caused by linearly combining the common factor and
idiosyncratic terms.
In this paper we propose an extended model, which overcomes this
problem. An extra idiosyncratic term is introduced which models
totally external default risk. Here one should think of default
events due to fraud, or legal issues. The most noticeable default
events over the last couple of years have been Enron, Worldcom and
Parmalat. All of these defaulted due to totally external causes.
The occurrence of such default events do not increase the
available information on the common factor driving correlated
defaults.
In addition it is shown that this extended model provides a
plausible explanation for the observed compound correlation smile,
or equivalently, the base correlation skew. Moreover, this model
requires two additional parameters with which one can control the
shape of the so-called base correlation skew.
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Double Default Correlation
Working Paper, July 2004
Abstract
Copula functions have become standard practice for pricing multi-name credit derivatives. Marginal
default distributions are often chosen by using a simple deterministic intensity function. It is wellknown
that this approach only generates default time correlation and, apart from jumps due to
default events, does not generate correlation between the conditional default intensities, or the conditional
spreads. In this paper we consider pricing multi-name credit derivatives taking both default
time correlation as well as default intensity correlation into account. This is achieved by defining two
common factors, one for each type of correlation.
Further, we derive a fast way to price conditional on default events or survival for the one-factor
model. Default and survival information is translated to information on the common factor. This
approach allows us to graph conditional default intensities, or conditional CDS spreads, for simulated
scenarios. These simulations show that our model results in a more realistic behavior of the
conditional CDS spreads as one can distinguish both credit spread correlation as well as jumps in
case of correlated default events.
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Implied Modelling
MSc Thesis, March 2000
Internship at Mees Pierson
Abstract
In this thesis we analyse different implied models for valuing plain vanilla options.
It is shown how the standard numerical techniques can be adapted in
such a way that a set of options will be priced consistent with their market values.
First the binomial and trinomial trees are considered, after which we will show how the
finite difference approach can be used. For the trinomial tree and the finite difference method one
can use two methods. Either parameters are chosen such that option prices are matched exactly, or
one can use the local volatility function. We analyse the convergence of model prices to observed
market quotes and compare these between the models.
We show the implications of using the implied model on the greeks and on the prices of exotic options,
such as barrier options.
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