**
Model risk for equity derivatives
**

Frank Bervoets

Site of the project:

Rabobank International

Croeselaan 18

3521 CB Utrecht

start of the project:
Februari 2006
br>

The Master project has been finished in September 2006
by the completion of the
Masters Thesis and a final
presentation has been given.
For working address etc. we refer to our
alumnipage.

**Summary of the master project:**

The goal of this MSc project is to assess the model risk of equity
derivatives, in both a quantitative and qualitative manner. We will
assume
that the reality is described adequately by a certain model, e.g. the
Heston
stochastic volatility model.

First of all, an fast Fourier transform (FFT) based quadrature pricing
technique is developed, and the numerical errors made are estimated.
The
one-dimensional quadrature pricing will allow us to price callable
exotics in
the one-dimensional affine Levy models. Secondly, as we will most
probably be
using the Heston model as realityâ, the quadrature pricing
technique is
extended to two dimensions, as the model is two-dimensional (the
dimensions
being the stock price and the stochastic variance). This will allow us
to
price purely callable exotics in several stochastic volatility models.

The second step is to calibrate a whole host of models, of both the
local
volatility and affine Levy type, to this real volatility
surface. Finally,
we will price exotic derivatives in all these models, and compare the
resulting prices to reality.
When talking about model risk, we have to distinguish intra- and
inter-model
risk. We define intra-model risk for a certain contract as the maximum
price
difference we can obtain within one model, given that this model is
calibrated to the initial volatility surface. Such differences can
arise due
to using different starting values for the parameters in an implied
calibration. Inter-model risk is the traditional model risk, i.e. the
maximum
price difference over various (ideally all) models, given that all
models are
adequately calibrated to the initial volatility surface.
## Contact information:
Kees
Vuik

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