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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/
- Published: 2023-01-25T18:00:53.000Z
- Updated: 2026-05-16T22:39:04.000Z
- Author: Dr. Dragos Bozdog
- Tags: 2018, #Import 2024-05-30 10:26, #Import 2025-11-08 22:14

**Author:** Dimitrios Kostakis  
**Degree:** M.S. in Financial Engineering  
**Year:** 2018  
**Advisory Committee:** Dr. Thomas Monza Lonon, Dr. Ionut Florescu

**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, choosing 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.