Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Wednesday, June 6, 2018
11:10 a.m.
BA6183

PhD Candidate:  Julio Hernandez Bellon
Supervisor:   Luis Seco
Thesis title: Correlation Model Risk and Non Gaussian Factor Models

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Abstract:

Two problems are considered in this thesis. The first one is concerned with correlation model risk and the second one with non Gaussian factor modeling of asset returns.

One of the fundamental problems in the application of mathematical finance results in a real world setting, is the dependence of mathematical models on parameters (correlations) that are hard to observe in markets. The common term for this problem is model risk. The first part of this thesis aims to provide some building blocks in the estimation of the sensitivities of mathematical objects (prices) to correlation inputs. In high dimensions, computational complexities increase faster than exponentially, a typical approach to deal with this problem is to introduce a principal component approach for dimension reduction. We consider the price of portfolios of options and approximations obtained by modifying the eigenvalues of the covariance matrix, then proceed to
find analytical upper bounds of the magnitude of the difference between the price and the approximation, under
different assumptions. Monte Carlo simulations are then used to plot the difference between the price and the
approximation.

In the second part of this thesis the assumptions and estimation methods of four different factor models with
time varying parameters are discussed. These models are based on Sharpe’s single index model, the first one
assumes that residuals follow a Gaussian white noise process, while the other three approaches combine the
structure of a single factor model with time varying parameters, with dynamic volatility (GARCH) assumptions
on the model components. The four approaches are then used to estimate the time varying alphas and betas of
three different hedge fund strategies and results are compared.

A copy of the thesis can be found here:  Thesis_Julio_Hernandez_07_30

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