The closed-form option pricing formulas under the sub-fractional Poisson volatility models

A new fractional process called the sub-fractional Poisson process N-H (t) is proposed, which has continuous sample paths, long- memory, leptokurtosis and heavy tail distribution, is of convenience to price options and simulate the variance process of risk asset return. Based on the sub-fractional Poisson process N-H (t) the new fractional variance processes have been proposed, which may capture the skewness and the long-memory as well as mean-reverting in the stock price volatilities. In particular, the characteristic function method for option pricing is given, and the analytical formulas for European option price C(t, S-t) have been obtained under the risk-neutral probability measure. (C) 2021 Elsevier Ltd. All rights reserved.