Equity-Linked Securities Option Pricing By Fractional Brownian Motion

In this paper, we use the Monte Carlo simulation (MCS) method to price the Equity-Linked Securities (ELS) option by fractional Brownian motion (fBm). We use the fBm that satisfy the Ito process instead of the geometric Brownian motion, and we call the proposed model ELS-fBm model. We first do the con-vergence test with the number of MCS. Then, we price the one-, two-, and three-asset ELS by employing the classical ELS model and the ELS-fBm model, respectively. We see that the price of ELS varies with different Hurst exponent, which indicates that the ELS pricing model considering the long-range depen-dence is necessary and more suitable for the financial market under uncertain environment. In addition, we prove the superiority of our proposed model with an actual three-assets ELS product which is issued by Future Asset company. We find the ELS price calculated by the proposed ELS-fBm model almost the same as the ELS price in the ELS product contract issued by Future Asset company, while the classical ELS model produces a great deviation.(C) 2021 Elsevier Ltd. All rights reserved.