American call option pricing under the KoBoL model with Poisson jumps

Beng Feng; Congyin Fan; Beng Feng; Congyin Fan

doi:10.3934/nhm.2025009

Networks and Heterogeneous Media

2025, Volume 20, Issue 1: 143-164. doi: 10.3934/nhm.2025009

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Research article

American call option pricing under the KoBoL model with Poisson jumps

Beng Feng ^1,2,
Congyin Fan ^{1
,
,}

1.
School of Economics and Finance, Guizhou University of Commerce, Guiyang 550014, China
2.
Faculty of Finance, City University of Macau, Macau 999078, China

Received: 08 October 2024 Revised: 11 January 2025 Accepted: 07 February 2025 Published: 20 February 2025

In the case of the KoBoL model with the jump process (KoBoLJ), the pricing problem of American call option is investigated in this paper. The pricing model of this kind of financial derivatives is a free boundary problem with a fractional-partial-integro-differential equation (FPIDE). In fact, it is impossible to obtain the analytical solution of the mathematical model. Hence, the mathematical model with free boundary should be changed as a fixed one and then the numerical scheme is set to solve the transformed model. In the proposed approach, we proved that the American call option values obtained by the current method are not lower than the intrinsic values of this option. Moreover the PCGNR method with the fast Fourier transform (FFT) technique was employed to handle the semi-globalness of the fractional-integro operator. The significant effects of the parameters in our model on the optimal exercise price curve ware analyzed.
- KoBoL model,
- jump diffusion,
- option pricing,
- PCGNR method,
- penalty method
Citation: Beng Feng, Congyin Fan. American call option pricing under the KoBoL model with Poisson jumps[J]. Networks and Heterogeneous Media, 2025, 20(1): 143-164. doi: 10.3934/nhm.2025009

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Abstract

In the case of the KoBoL model with the jump process (KoBoLJ), the pricing problem of American call option is investigated in this paper. The pricing model of this kind of financial derivatives is a free boundary problem with a fractional-partial-integro-differential equation (FPIDE). In fact, it is impossible to obtain the analytical solution of the mathematical model. Hence, the mathematical model with free boundary should be changed as a fixed one and then the numerical scheme is set to solve the transformed model. In the proposed approach, we proved that the American call option values obtained by the current method are not lower than the intrinsic values of this option. Moreover the PCGNR method with the fast Fourier transform (FFT) technique was employed to handle the semi-globalness of the fractional-integro operator. The significant effects of the parameters in our model on the optimal exercise price curve ware analyzed.

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