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A Generalized Asset Pricing Model Based on Alpha-Stable Distributions

Ayyoubzadeh, Mohsen | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57628 (44)
  4. University: Sharif University of Technology
  5. Department: Management and Economics
  6. Advisor(s): Talebian, Masoud
  7. Abstract:
  8. Many theoretical and empirical studies in finance explicitly or implicitly rely on the Gaussian distribution assumption for the variables under consideration. This assumption is applied in various ways, from its use as the basis for deriving the optimal portfolio composition in the classical Markowitz framework to statistical tests assessing the significance of different variables effects in various regressions. Despite extensive empirical evidence supporting the non-Gaussian distribution of returns in stock markets, there is still a gap in achieving a comprehensive model to replace the Gaussian assumption across all areas of financial studies. In this study, alpha-stable distributions are investigated as a suitable candidate to explain certain characteristics of financial data. Using the properties of stochastic differential equations for Levy processes, a pricing model is developed to allow for the use of this hypothesis as an alternative to the Gaussian distribution. In developing this model, unnecessary assumptions are avoided as much as possible, and the proposed method is designed to be flexible enough to accommodate many other distributions. Finally, several numerical benchmarks are conducted to compare the explanatory power of cross-sectional returns based on the model developed in this study with the classical Capital Asset Pricing Model (CAPM), using traded securities in the Tehran Stock Exchange over various time horizons
  9. Keywords:
  10. Stochastic Differential Equation ; Stock Return ; Optimal Portfolio ; Cross-Sectional Analysis ; Non-Gaussian Regression