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# A LOG-MIXED GAUSSIAN JUMP DIFFUSION MODEL: NUMERICALLY PRICING AMERICAN AND EUROPEAN OPTIONS AND ANALYZING CALIBRATION TECHNIQUES
- URL: https://fsc.stevens.edu/a-log-mixed-gaussian-jump-diffusion-model-numerically-pricing-american-and-european-options-and-analyzing-calibration-techniques-2/
- Published: 2026-02-16T16:22:16.000Z
- Updated: 2026-05-16T22:32:53.000Z
- Description: In this thesis we model the asset price using jump diffusion with a log mixed Gaussian distribution as the jump size. This jump diffusion model follows a Partial Integro Differential Equation (PIDE).
- Author: Peterson Iyayi Inneh
- Tags: masters-thesis

**Author:** Dimitrios Kostakis 

**Advisor:** [Dr. Thomas Monza Lonon ](https://search.stevens.edu/s/search.html?query=Thomas+Monza+Lonon&f.Tabs%7C21772%7Eds-sit-people=People&collection=21772%7Esp-search&sort=&ref=fsc.stevens.edu)

**Date:** May 11, 2018 

**Department:** Financial Engineering 

**Degree:** Master of Science- Financial Engineering

**Advisory Committee:**

[Dr. Thomas Monza Lonon](https://search.stevens.edu/s/search.html?query=Thomas+Monza+Lonon&f.Tabs%7C21772%7Eds-sit-people=People&collection=21772%7Esp-search&sort=&ref=fsc.stevens.edu), Advisor Date 

[Dr. Ionut Florescu](https://www.stevens.edu/profile/ifloresc?ref=fsc.stevens.edu), Reader

**Abstract:** In this thesis we model the asset price using jump diffusion with a log mixed Gaussian distribution as the jump size. This jump diffusion model follows a Partial Integro Differential Equation (PIDE). We calibrate the model using a variety of techniques including clustering and the EM-Algorithm using historical log returns for equity stocks and indices. To further calibrate the model we then investigate risk neutral pricing by fitting λ using at-the-money (ATM) derivative options. Finally, choos ing the best set of calibrated parameters we implement numerical methods to price American and European options. An explicit finite difference scheme is implemented by discretizing the PIDE. 

For full Dissertation, click [here](https://www.proquest.com/pqdtlocal1007352/docview/2068024112/94362B353B864FA9PQ/1?accountid=14052&sourcetype=Dissertations%20&%20Theses&ref=fsc.stevens.edu).