Analytical Solvability and Exact Simulation in Models with Affine Stochastic Volatility and Levy Jumps

46 Pages Posted: 21 Oct 2022 Last revised: 9 Nov 2022

See all articles by Pingping Zeng

Pingping Zeng

Southern University of Science and Technology

Ziqing Xu

affiliation not provided to SSRN

Pingping Jiang

Nankai University - School of Mathematical Sciences

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: October 12, 2022

Abstract

In this paper, we investigate the analytical solvability of models with affine stochastic volatility and Levy jumps by deriving a unified formula for the conditional moment generating function of the log-asset price and showing the condition under which this new formula is explicit. The results lay a foundation for a range of valuation, calibration, and econometric problems. We then combine our theoretical results, the Hilbert transform method, various interpolation techniques, with the dimension reduction technique to propose unified simulation schemes for solvable models with affine stochastic volatility and Levy jumps. In contrast to traditional exact simulation methods, our approach is applicable to a broad class of models, maintains good accuracy, and enables efficient pricing of discretely monitored path-dependent derivatives. We analyze various sources of errors arising from the simulation approach and present error bounds. Finally, extensive numerical results demonstrate that our method is highly accurate, efficient, simple to implement, and widely applicable.

Keywords: analytical solvability, exact simulation, stochastic volatility, Levy jumps, Hilbert transform method, interpolation, path-dependent derivatives

JEL Classification: C

Suggested Citation

Zeng, Pingping and Xu, Ziqing and Jiang, Pingping and Kwok, Yue Kuen, Analytical Solvability and Exact Simulation in Models with Affine Stochastic Volatility and Levy Jumps (October 12, 2022). Available at SSRN: https://ssrn.com/abstract=4245455 or http://dx.doi.org/10.2139/ssrn.4245455

Pingping Zeng (Contact Author)

Southern University of Science and Technology ( email )

1088 Xueyuan Avenue
Nanshan District
Shenzhen, Guangdong
China

Ziqing Xu

affiliation not provided to SSRN

Pingping Jiang

Nankai University - School of Mathematical Sciences ( email )

Weijin Road #94
Tianjin, 300071
China

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

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