Shot-noise cojumps: exact simulation and option pricing

Yan Qu, Angelos Dassios and Hongbiao Zhao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 (search for similar items in EconPapers)
JEL-codes: C15 C63 G13 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2023-03-01
New Economics Papers: this item is included in nep-mfd and nep-rmg
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Published in Journal of the Operational Research Society, 1, March, 2023, 74(3), pp. 647 - 665. ISSN: 1476-9360

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