Can a novel approach enhance financial risk assessment? This paper explores the use of the truncated Levy process (TLP) for financial modeling and option theory, presenting a promising alternative to traditional methods. The TLP accounts for excess kurtosis at short timescales and slow convergence to Gaussian at longer timescales, addressing limitations of Levy processes. The study tests the TLP paradigm using high-frequency data from the Australian All Ordinaries share market index. It then considers an optimal option hedging strategy tailored for the early Levy-dominated regime and compares it with the standard delta hedging approach. The results indicate significant differences between the two strategies, highlighting the potential benefits of the TLP-based approach. These findings suggest that the truncated Levy process offers a valuable tool for financial analysts and risk managers, providing a more accurate representation of financial dynamics and enabling more effective option hedging strategies. The research contributes to the ongoing development of sophisticated models for navigating the complexities of modern financial markets.
Published in the International Journal of Theoretical and Applied Finance, this paper aligns with the journal's focus on cutting-edge research in financial modeling, derivatives pricing, and risk management. By exploring the use of the truncated Levy process for option theory, the research contributes to innovative approaches for understanding and managing financial risk, fitting well within the journal's scope.