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

  • Feng Xu EMAIL logo
Veröffentlicht/Copyright: 3. September 2020
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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.


Supported by the Fundamental Research Funds for Suzhou Vocational University of China (SVU2018YY01) and “QINGLAN” project of SVU


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Received: 2019-11-16
Accepted: 2020-06-01
Published Online: 2020-09-03
Published in Print: 2020-08-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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