Dissertations, Theses, and Capstone Projects
Date of Degree
9-2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy
Program
Economics
Advisor
Christos Giannikos
Committee Members
Wim P. M. Vijverberg
Yochanan Shachmurove
S. R. Srinivasa Varadhan
Subject Categories
Economics | Finance
Keywords
Large deviations, Tail risk, Gamma difference distribution, CGMY model, Characteristic function estimation, Option
Abstract
This dissertation develops a unified, computationally tractable framework for modeling as- set returns beyond the Gaussian benchmark, built on the Gamma Difference Distribution (GDD) and the theory of large deviations. The dissertation makes four substantive con- tributions. First, we generalize the Gaussian-copula credit risk framework of Pham (2007) to a Gamma copula driven by compound Poisson processes and derive its large-deviation rate function in closed form, capturing the asymmetric, heavy-tailed dependence that the Gaussian copula excludes; in the same framework we derive closed-form rate functions for the GDD and CGMY L´evy processes. Second, I develop a trigonometric moment estima- tor for the GDD that reduces estimation to four algebraic equations obtained by matching the empirical characteristic function at two frequencies; the estimator is an exactly identified generalized method of moments procedure with a bounded moment function, and is therefore consistent and asymptotically normal without any moment restrictions on the data. Third, I apply the estimator to United States equity, corporate bond, and real estate returns: the GDD materially improves on the lognormal benchmark for equities and real estate, while the lognormal remains adequate for investment-grade bonds, demonstrating that the method is discriminating rather than mechanical. Fourth, I apply the GDD framework to European call option pricing, deriving a closed-form risk-neutral (Esscher) tilt and a tractable pric- ing formula that nests the Black–Scholes and Variance Gamma models, and generates the empirically observed volatility smile with a steeper left-tail skew than the Variance Gamma benchmark. Throughout, the large-deviation rate function ties the estimation and pricing results together: it quantifies the exponential decay of extreme-loss probabilities and of deep out-of-the-money option prices under the fitted models.
Recommended Citation
Saha, Shree Rajkumar, "Non-Gaussian Models for Asset Returns: The Gamma Difference Distribution, Parameter Estimation, Option Pricing, and Large Deviation Theory" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6924
