TY - JOUR
T1 - Parameter Estimation for Geometric Lévy Processes with Constant Volatility
AU - Chhetri, Sher
AU - Long, Hongwei
AU - Ball, Cory
N1 - Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2024
Y1 - 2024
N2 - In finance, various stochastic models have been used to describe price movements of financial instruments. Following the seminal work of Robert Merton, several jump-diffusion models have been proposed for option pricing and risk management. In this study, we augment the process related to the dynamics of log returns in the Black–Scholes model by incorporating alpha-stable Lévy motion with constant volatility. We employ the sample characteristic function approach to investigate parameter estimation for discretely observed stochastic differential equations driven by Lévy noises. Furthermore, we discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. To further demonstrate the validity of the estimators, we present simulation results for the model. The utility of the proposed model is demonstrated using the Dow Jones Industrial Average data, and all parameters involved in the model are estimated. In addition, we delved into the broader implications of our work, discussing the relevance of our methods to big data-driven research, particularly in the fields of financial data modeling and climate models. We also highlight the importance of optimization and data mining in these contexts, referencing key works in the field. This study thus contributes to the specific area of finance and beyond to the wider scientific community engaged in data science research and analysis.
AB - In finance, various stochastic models have been used to describe price movements of financial instruments. Following the seminal work of Robert Merton, several jump-diffusion models have been proposed for option pricing and risk management. In this study, we augment the process related to the dynamics of log returns in the Black–Scholes model by incorporating alpha-stable Lévy motion with constant volatility. We employ the sample characteristic function approach to investigate parameter estimation for discretely observed stochastic differential equations driven by Lévy noises. Furthermore, we discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. To further demonstrate the validity of the estimators, we present simulation results for the model. The utility of the proposed model is demonstrated using the Dow Jones Industrial Average data, and all parameters involved in the model are estimated. In addition, we delved into the broader implications of our work, discussing the relevance of our methods to big data-driven research, particularly in the fields of financial data modeling and climate models. We also highlight the importance of optimization and data mining in these contexts, referencing key works in the field. This study thus contributes to the specific area of finance and beyond to the wider scientific community engaged in data science research and analysis.
KW - Alpha-stable Lévy motion
KW - Constant volatility
KW - Geometric Lévy processes
KW - Parameter estimation
KW - Sample characteristic function
UR - http://www.scopus.com/inward/record.url?scp=85183670941&partnerID=8YFLogxK
U2 - 10.1007/s40745-024-00513-8
DO - 10.1007/s40745-024-00513-8
M3 - Article
AN - SCOPUS:85183670941
SN - 2198-5804
JO - Annals of Data Science
JF - Annals of Data Science
ER -