Stochastic Modeling of Earthquakes and Option Pricing Using BNS-Gamma-OU Model
High frequency data are becoming increasingly popular these days. They are fundamental in basically every facet of people’s lives. They are the determining factors in hedging in the field of finance. In geology, they help in the accurate prediction of earthquakes’ magnitude which goes along way to help save lives and properties. High frequency data are also used more and more frequently for speculations. For this reason, it is important not only for scientists to apply models allowing correct quantification of these data, but also to improve the efficiency of these models. The Black-Scholes model, which is widely used because of its simplicity and comprehensiveness has so many drawbacks that a lot of literature has covered. Although Black-Scholes will undoubtedly continue to be useful for a very long time, it is clear that the model underlying its use is strongly at odds with the observed data. The simulation of high frequency data has become essential in this fast paced world. The quest to predict the path of these kind of data in finance is essential to be able to curb loses or maximize profit in the field of seismic modeling. It is prudent to be able to find the magnitude of earthquake at any given time because of the numerous negative impact it has on properties and lives. These kinds of data are volatile which, makes them very difficult to simulate. The Gamma-OU model and Black-Scholes model are known to be used to predict the path of earthquakes and stock-prices, respectively. The Gamma-OU works well with earthquake data, while the Black-Scholes model functions very well with option pricing. This study is to present how to predict the path of high frequency data using the Barndorff-Nielsen and Shephard model with the Gamma-OU process and demonstrate that it is superior to the Gamma-OU model.
Quashie, Mandela Bright, "Stochastic Modeling of Earthquakes and Option Pricing Using BNS-Gamma-OU Model" (2020). ETD Collection for University of Texas, El Paso. AAI28030276.