Events
Department of Mathematics and Statistics
Texas Tech University
Understanding and effectively modeling the volatility of speculative assets play a crucial role in making informed investment decisions. As Bitcoin is increasingly perceived as a potential alternative to traditional fiat currencies, its unique volatility characteristics become a focal point for investors. Therefore, it is imperative to gain a comprehensive understanding and employ suitable models to capture the dynamics governing Bitcoin's volatility.
In this presentation, we delve into the analysis of Bitcoin's volatility using Double Subordinated Models. Our primary focus is on introducing a double subordinated Levy process known as the Normal Double Inverse Gaussian (NDIG) to effectively model the time series properties of the cryptocurrency. Additionally, we present an innovative arbitrage-free option pricing model based on the NDIG process, offering a fresh perspective on the valuation of Bitcoin.
Within the framework of this model, we derive two distinct measures of Bitcoin volatility. The first measure involves combining NDIG option pricing with the Chicago Board Options Exchange VIX model, providing an implied volatility measure that reflects the perspectives of options traders. The second measure delves into implied volatility in the practical world, considering the viewpoints of spot traders and utilizing an intrinsic time formulation.
Both volatility measures are systematically compared to a historical standard deviation-based volatility metric. Notably, with appropriate linear scaling, the NDIG process demonstrates a remarkable capability to accurately capture the observed in-sample volatility of Bitcoin. This presentation aims to contribute valuable insights into comprehending and modeling Bitcoin's volatility dynamics using the powerful framework of Double Subordinated Models.
This Departmental Job Candidate Colloquium is sponsored by the Mathematical Finance seminar group and may be attended virtually at 2:00 PM (UT-6) via this Zoom link.
abstract pdf
This Departmental Job Candidate Colloquium is sponsored by the Statistics seminar group and may be attended virtually at 2:00 PM (UT-6) via this Zoom link.
Variational methods have formed the foundation of classical mechanics for several hundred years. In recent years, these methods have become much more powerful through the applications of the geometric approach. In this lecture, I will show how these geometric methods can give deep insights into seemingly disconnected problems using the same mathematical principles. After a general and gentle introduction, I will illustrate this method on the examples of modeling figure skating (a system with nonholonomic constraint) and fluid-structure interactions, in particular, the dynamics of a porous media containing incompressible fluid (two media coupled through the incompressibility constraint). I will also outline the further potential of the method by briefly mentioning new applications of these methods to computations based on physics-based neural networks. I will also discuss the limitations of these methods, i.e., what progress can be achieved by algorithmic thinking alone and at what point ingenuity and creativity must take over.
This Job Candidate Departmental Colloquium is sponsored by the Applied Math seminar group and may be attended in person in ESB1-120 and virtually at 2:00 PM (UT-6) via this Zoom link. This interview will be available in the TTU Mediasite Catalog.
Meeting ID: 947 9013 5459
Passcode: Math