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FINANCIAL MODELING WITH LE ́VY PROCESSES AND APPLYING LE ́VY SUBORDINATOR TO CURRENT STOCK DATA

Abstract Details

2019, Doctor of Philosophy, Case Western Reserve University, Mathematics.
The normal distribution for financial modeling is frequently encountered, but it is not a good model when the data behavior is skewed and has fat-tailed properties. It is often wrong to employ distributions which have symmetric and rapidly decreasing tail properties. The properties of the α-stable distribution are important 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 modifications for Brownian-type processes are obtained via the introduction of a time-changed Brownian model. This extension is related to replacement of the real-time in Brownian systems by a non-decreasing L ́evy process (called subordinator). In this thesis, we analyze a process related to a subordinated Brownian motion which is called a normal tempered subordinator and also is described as a Brownian motion with drift driven by a tempered stable subordinator. We compare the main statistical analysis of the TSB (Subordinate tempered stable process to Brownian motion) process and diffusive process. In this work, 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.
Wojbor Woyczynski (Advisor)
185 p.

Recommended Citations

Citations

  • ALMEIDA, G. S. (2019). FINANCIAL MODELING WITH LE ́VY PROCESSES AND APPLYING LE ́VY SUBORDINATOR TO CURRENT STOCK DATA [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1568306440126471

    APA Style (7th edition)

  • ALMEIDA, GONSALGE. FINANCIAL MODELING WITH LE ́VY PROCESSES AND APPLYING LE ́VY SUBORDINATOR TO CURRENT STOCK DATA. 2019. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1568306440126471.

    MLA Style (8th edition)

  • ALMEIDA, GONSALGE. "FINANCIAL MODELING WITH LE ́VY PROCESSES AND APPLYING LE ́VY SUBORDINATOR TO CURRENT STOCK DATA." Doctoral dissertation, Case Western Reserve University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1568306440126471

    Chicago Manual of Style (17th edition)