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 reality‚, 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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