Abstract
A new fractional process called the sub-fractional Poisson process NH(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 NH(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,St) have been obtained under the risk-neutral probability measure.
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