Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model

Rehez Ahlip; Laurence A. F. Park; Ante Prodan

doi:10.33187/jmsm.432019

EN

Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model

Abstract

We examine European call options in the jump-diffusion version of the Double Heston stochastic volatility model for the underlying price process to provide a more flexible model for the term structure of volatility. We assume, in addition, that the stochastic interest rate is governed by the Cox-- Ross -- Ingersoll (CIR) dynamics. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the European call option in the hybrid call option/interest rates model. Numerical results show that the model implied volatilities are comparable for in-sample but outperform out-of-sample implied volatilities compared to the benchmark Heston model[1], and Double Heston volatility model put forward by Christoffersen et al., [2] for calls on the S&P 500 index.

Keywords

Finance,Double Heston Jump Diffusion model,L\'evy process,Affine processes,Calibration of stochastic volatility

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Rehez Ahlip ^* This is me
Australia

Laurence A. F. Park This is me
Australia

Ante Prodan
0000-0001-9684-7967
Australia

Publication Date

December 30, 2018

Submission Date

June 8, 2018

Acceptance Date

September 26, 2018

Published in Issue

Year 2018 Volume: 1 Number: 3

DOI

https://doi.org/10.33187/jmsm.432019

IZ

https://izlik.org/JA26DF82WP

APA

Ahlip, R., Park, L. A. F., & Prodan, A. (2018). Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model. Journal of Mathematical Sciences and Modelling, 1(3), 138-152. https://doi.org/10.33187/jmsm.432019

AMA

1.Ahlip R, Park LAF, Prodan A. Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model. Journal of Mathematical Sciences and Modelling. 2018;1(3):138-152. doi:10.33187/jmsm.432019

Chicago

Ahlip, Rehez, Laurence A. F. Park, and Ante Prodan. 2018. “Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model”. Journal of Mathematical Sciences and Modelling 1 (3): 138-52. https://doi.org/10.33187/jmsm.432019.

EndNote

Ahlip R, Park LAF, Prodan A (December 1, 2018) Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model. Journal of Mathematical Sciences and Modelling 1 3 138–152.

IEEE

[1]R. Ahlip, L. A. F. Park, and A. Prodan, “Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, pp. 138–152, Dec. 2018, doi: 10.33187/jmsm.432019.

ISNAD

Ahlip, Rehez - Park, Laurence A. F. - Prodan, Ante. “Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model”. Journal of Mathematical Sciences and Modelling 1/3 (December 1, 2018): 138-152. https://doi.org/10.33187/jmsm.432019.

JAMA

1.Ahlip R, Park LAF, Prodan A. Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model. Journal of Mathematical Sciences and Modelling. 2018;1:138–152.

MLA

Ahlip, Rehez, et al. “Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, Dec. 2018, pp. 138-52, doi:10.33187/jmsm.432019.

Vancouver

1.Rehez Ahlip, Laurence A. F. Park, Ante Prodan. Semi-Analytical Option Pricing Under Double Heston Jump-Diffusion Hybrid Model. Journal of Mathematical Sciences and Modelling. 2018 Dec. 1;1(3):138-52. doi:10.33187/jmsm.432019