Bifractional Black-Scholes Model for Pricing European Options and Compound Options

Xu Feng ()
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Xu Feng: School of Business, Suzhou Vocational University, Suzhou, 215400, China

Journal of Systems Science and Information, 2020, vol. 8, issue 4, 346-355

Abstract: Recent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

Keywords: bifractional Brownian motion; compound options; long memory property; pricing model (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:8:y:2020:i:4:p:346-355:n:4

DOI: 10.21078/JSSI-2020-346-10

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