离散时间亚分数布朗运动机制下的欧式期权定价

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2023-12-22 DOI:10.3390/fractalfract8010013

Zhidong Guo, Yang Liu, Linsong Dai

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引用次数: 0

摘要

本文给出了亚分数布朗运动二阶矩增量的近似静止性。在此基础上，建立了离散时间亚分数布朗机制下的欧式期权定价模型。分别给出了三角对冲策略和混合对冲策略下欧式期权的定价公式。此外，三角对冲下的欧式看涨期权定价要大于混合对冲。通过数值实验证明，混合对冲的对冲误差率小于三角对冲。

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

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.

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.