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Option pricing in a subdiffusive constant elasticity of variance (CEV) model

Kevin Z. Tong

Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada

E-mail Address: ztong043@uottawa.ca

Corresponding author.

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and

Allen Liu

Enterprise Risk and Portfolio Management, Bank of Montreal, First Canadian Place, Toronto, Ontario, M5X 1A3, Canada

E-mail Address: Allen.Liu@bmo.com

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https://doi.org/10.1142/S242478631950018XCited by:1 (Source: Crossref)

Abstract

In this paper, we extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse $α$ -stable subordinator. The new model can capture the subdiffusive characteristics of financial markets. We find the corresponding fractional Fokker–Planck equation governing the PDF of the new process. We also derive the analytical formula for option prices in terms of eigenfunction expansion. This method avoids the evaluation of PDF of an inverse $α$ -stable variable and also eliminates the need for numerical integration to calculate the option prices. We numerically investigate the sensitivities of the option prices to the key parameters of the newly developed model.

Keywords:

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