# PhD Thesis Defense: Gonsalge Sureka Almeida

Friday June 14, 2019 at 10:00 a.m.

Title: Financial Modeling with LE ́VY Processes and Applying LE ́VY Subordinator to Current Stock Data

Thesis Advisor: Dr. Wojbor Woycznksi

Abstract

The normal distribution for financial modeling with assets returns are frequently encountered, but it is not a good model when the data behavior is skewed and has fat-tailed properties. It is often wrong the distribution which has symmetric and rapidly decreasing tail properties. The properties of the $\alpha$-stable distribution are impressive to statisticians for modeling the data for skewness and fat tails. In order to obtain a well-defined model for pricing options, the mean, variance, and exponential moments of the return distribution often cannot be considered. For this reason, tempered stable distributions have been proposed for financial modeling. Other possibilities of modification for Brownian-type processes is the introduction of a time-changed Brownian model. In this extension is related to replacement of the real-time in Brownian systems by non-decreasing Le’vy process (called subordinator). In this thesis, we analyze a process related to subordinated Brownian motion which is called normal tempered subordinator and also describes as a Brownian motion with drift driven by tempered stable subordinator. We compare the main statistical analysis of the TSB(Subordinate the tempered stable process to the Brownian motion) process and diffusive process. In here, we mention the two techniques of a parameter’s estimation procedures and validate them. In order to show the usefulness of theoretical results, we analyze the system using the real-stock data.

*Reception to follow at 12:15pm in Yost Hall #207