Document Type


Date of Degree

Fall 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Palle Jorgensen


Derivative pricing, model calibration, and sensitivity analysis are the three main problems in financial modeling. The purpose of this study is to present an algorithm to improve the pricing process, the calibration process, and the sensitivity analysis of the double Heston model, in the sense of accuracy and efficiency. Using the optimized caching technique, our study reduces the pricing computation time by about 15%. Another contribution of this thesis is: a novel application of the Automatic Differentiation (AD) algorithms in order to achieve a more stable, more accurate, and faster sensitivity analysis for the double Heston model (compared to the classical finite difference methods). This thesis also presents a novel hybrid model by combing the heuristic method Differentiation Evolution, and the gradient method Levenberg--Marquardt algorithm. Our new hybrid model significantly accelerates the calibration process.


automatic differentiation, calibration, derivative pricing, gradient-based method, heuristic optimization method, stochastic volatility


viii, 110 pages


Includes bibliographical references (pages 108-110).


Copyright © 2016 Ze Zhao