European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Abstract

In this paper, the approximate stationarity of the second-order moment increments of the sub-fractional Brownian motion is given. Based on this, the pricing model for European options under the sub-fractional Brownian regime in discrete time is established. Pricing formulas for European options are given under the delta and mixed hedging strategies, respectively. Furthermore, European call option pricing under delta hedging is shown to be larger than under mixed hedging. The hedging error ratio of mixed hedging is shown to be smaller than that of delta hedging via numerical experiments.

Keywords

• discrete-time model
• sub-fractional Brownian motion
• delta hedging
• mixed hedging
• hedging error ratio