زمان تغییر هندسی جزء به جزء حرکت براونی و انتخاب روش قیمت گذاری، با هزینه های معاملاتی

This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black–Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.

In this paper, we derive a generalized BS model whose price of underlying asset follows a time-changed geometric FBM. The time-change process is an inverse α-stable subordinator. Without using the arbitrage argument, a European call option pricing formula under transaction costs in discrete time setting is obtained. If H = 1 2 , the price model of the underlying asset degenerates to the model mentioned by Magdziarz [2], and if α ↑ 1, our result is consistent with the result in Ref. [11].