A fractional version of the Merton model.
type: Item
instance of: scholarly article
title: A fractional version of the Merton model.
zbMATH Open document ID: 1071.91024
DOI: 10.1016/S0960-0779(02)00109-1
author: Xiao-Tian Wang
author: Xiang-Qian Liang
author: Fuyao Ren
published in: Chaos, Solitons and Fractals
publication date: 2004-01-14T00:00:00Z
review text: In this paper, the impact of long-range dependence on the option pricing is investigated. The authors consider the option pricing problem while the dynamics of stock log-price follow a fractional jump-diffusion process with Hurst exponent \(H>1/2\). So, the sample paths of log-prices of the stocks exhibit long-range dependence and look as if they are fractional Brownian motions, although occasional jumps will be noticeable. The price of a European call option is derived. It does not contain explicitly the volatility, therefore the call premiums are ``smaller'' than those of the Merton's call. Finally, the relation between Hurst exponent and long-range dependence is discussed.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 2027019
zbMATH Keywords: option pricing
zbMATH Keywords: long-range dependence
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2027019