Shot-Noise Cojumps: Exact Simulation and Option Pricing

Journal of the Operational Research Society, 74(3), 647-665​, 2023

36 Pages Posted: 1 Jun 2022 Last revised: 28 Jul 2023

See all articles by Yan Qu

Yan Qu

University of Warwick - Department of Statistics

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: May 23, 2022

Abstract

We consider a parsimonious framework of jump-diffusion models for price dynamics with stochastic price volatilities and stochastic jump intensities in continuous time. They account for conditional heteroscedasticity and also incorporate key features appearing in financial time series of price volatilities and jump intensities, such as persistence of contemporaneous jumps (cojumps), mean reversion and feedback effects. More precisely, the stochastic variance and stochastic intensity are jointly modelled by a generalised bivariate shot-noise process sharing common jump arrivals with any non-negative jump-size distributions. This framework covers many classical and important models in the literature. The main contribution of this paper is that, we develop a very efficient scheme for its exact simulation based on perfect decomposition where neither numerical inversion nor acceptance/rejection scheme is required, which means that it is not only accurate but also the efficiency would not be sensitive to the parameter choice. Extensive numerical implementations and tests are reported to demonstrate the accuracy and effectiveness of this scheme. Our algorithm substantially outperforms the classical discretisation scheme. Moreover, we unbiasedly estimate the prices of discrete-barrier European options to show the applicability and flexibility of our algorithms.

Keywords: Exact simulation, Monte Carlo simulation, Jump-diffusion models, Stochastic volatility models, Shot-noise process, Contemporaneous jumps, Cojumps, Shot-noise cojumps, Option pricing, Systemic risk

JEL Classification: 91G60

Suggested Citation

Qu, Yan and Dassios, Angelos and Zhao, Hongbiao, Shot-Noise Cojumps: Exact Simulation and Option Pricing (May 23, 2022). Journal of the Operational Research Society, 74(3), 647-665​, 2023, Available at SSRN: https://ssrn.com/abstract=4117276

Yan Qu

University of Warwick - Department of Statistics ( email )

Coventry, CV47AL
United Kingdom

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

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