A class of fourth-order Padé schemes for fractional exotic options pricing model

Ming-Kai Wang; Cheng Wang; Jun-Feng Yin; Ming-Kai Wang; Cheng Wang; Jun-Feng Yin

doi:10.3934/era.2022046

Electronic Research Archive

2022, Volume 30, Issue 3: 874-897. doi: 10.3934/era.2022046

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A class of fourth-order Padé schemes for fractional exotic options pricing model

School of Mathematical Sciences, Tongji University, Shanghai 200092, China

Academic Editor: Victor Barranca

Received: 30 December 2021 Revised: 06 February 2022 Accepted: 14 February 2022 Published: 02 March 2022

In order to reduce the oscillations of the numerical solution of fractional exotic options pricing model, a class of numerical schemes are developed and well studied in this paper which are based on the 4th-order Padé approximation and 2nd-order weighted and shifted Grünwald difference scheme. Since the spatial discretization matrix is positive definite and has lower Hessenberg Toeplitz structure, we prove the convergence of the proposed scheme. Numerical experiments on fractional digital option and fractional barrier options show that the (0, 4)-Padé scheme is fast, and significantly reduces the oscillations of the solution and smooths the Delta value.
- fractional option pricing model,
- Padéschemes,
- 4th-order schemes,
- exotic option
Citation: Ming-Kai Wang, Cheng Wang, Jun-Feng Yin. A class of fourth-order Padé schemes for fractional exotic options pricing model[J]. Electronic Research Archive, 2022, 30(3): 874-897. doi: 10.3934/era.2022046

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Abstract

In order to reduce the oscillations of the numerical solution of fractional exotic options pricing model, a class of numerical schemes are developed and well studied in this paper which are based on the 4th-order Padé approximation and 2nd-order weighted and shifted Grünwald difference scheme. Since the spatial discretization matrix is positive definite and has lower Hessenberg Toeplitz structure, we prove the convergence of the proposed scheme. Numerical experiments on fractional digital option and fractional barrier options show that the (0, 4)-Padé scheme is fast, and significantly reduces the oscillations of the solution and smooths the Delta value.

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