Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps

Zeng，Pingping1; Xu，Ziqing1,2; Jiang，Pingping3; Kwok，Yue Kuen4

2023

10.1111/mafi.12387

Mathematical Finance   Impact Factor & Quartile

0960-1627

1467-9965

We investigate analytical solvability of models with affine stochastic volatility (SV) and Lévy jumps by deriving a unified formula for the conditional moment generating function of the log-asset price and providing 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 SV and Lévy 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.

analytical solvability exact simulation Hilbert transform method interpolation Lévy jumps path-dependent derivatives stochastic volatility

SCI ; SSCI

English

First

National Natural Science Foundation of China["12171228","11701266"]

Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences

Business, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods

WOS:000963207200001

WILEY

ECONOMICS BUSINESS

2-s2.0-85152064379

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
2.Department of Mathematics,Hong Kong University of Science and Technology,Hong Kong
3.Center for Financial Engineering,Soochow University,Suzhou,China
4.Financial Technology Thrust,Hong Kong University of Science and Technology,Guangzhou,China

Zeng，Pingping,Xu，Ziqing,Jiang，Pingping,et al. Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps[J]. Mathematical Finance,2023,33(3).

Zeng，Pingping,Xu，Ziqing,Jiang，Pingping,&Kwok，Yue Kuen.(2023).Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps.Mathematical Finance,33(3).

Zeng，Pingping,et al."Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps".Mathematical Finance 33.3(2023).