Financial modeling with a tail-asymmetric truncated Lévy process

Abstract

The Lévy-stable stochastic process with asymmetric exponentially truncated tails is proposed as an alternative model for financial data. To demonstrate and develop the motivation for the model, the probability distribution of price fluctuations for the NIKKEI index at different timescales is analyzed and compared to Lévy-based stochastic processes commonly used for modeling price fluctuations. Common ground to Lévy-based models is that they try to capture properties such as power-law self-similarity at short timescales, convergence to a diffusion process for long timescales, and finite variance typically observed in real price fluctuations. It is shown that the proposed model is able to adapt to all such properties.