Electronic Thesis and Dissertation Repository

Thesis Format

Monograph

Degree

Master of Science

Program

Statistics and Actuarial Sciences

Supervisor

Escobar-Anel, Marcos

Abstract

We investigate portfolio optimization, risk management, and derivative pricing for a factor stochastic model that considers the 4/2 stochastic volatility on the common/systematic factor as well as on the intrinsic factor. This setting allows us to capture stochastic volatility and stochastic covariation among assets. The model is also a generalization of existing models in the literature as it includes the mean reverting property and spillover effect to capture wider types of financial assets. At a theoretical level we identify conditions for well-defined changes of measure. A quasi-closed form solution within a 4/2 structured model is obtained for a portfolio optimization problem. In the numerical section, a sensitivity analysis reveals a substantial impact on the implied volatility surface and risk measures level due to small changes in the 3/2 component b. In addition, commonality loading, spillover effect, and dependency among common factors are also influential with regards to implied volatility and risk measures.

Summary for Lay Audience

A Factor model is a financial model that employs some correlated factors or characteristics to explain or calculate a financial variable. In mathematical finance, factor models are widely used to model the relationship between asset returns and underlying risk factors. The goal of the model is to measure the expected return and forecast/manage security risk. Our model decomposes the risk across the market into common factors and intrinsic factors in a clear manner. Specifically, the common factors are exogenous (observable or not) variables explaining the systematic risk in the market, while the intrinsic factors relate to companies’ or asset's inherent risks. Moreover, each factor follows a 4/2 structured volatility process, which is a superposition of the well-known 1/2 Heston process and the 3/2 process brought up by Grasselli (2017). This setting allows us to capture stochastic volatility and stochastic covariation among assets. The model is also a generalization of existing models in the literature as it includes the mean reverting property and spillover effect to capture wider types of financial assets. In this thesis, we investigate portfolio optimization, risk management, derivative pricing, and sensitivity analysis on important parameters within this generalized 4/2 factor model.

Available for download on Monday, June 20, 2022

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