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Shot-noise cojumps: exact simulation and option pricing

Qu, Yan, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhao, Hongbiao (2023) Shot-noise cojumps: exact simulation and option pricing. Journal of the Operational Research Society, 74 (3). 647 - 665. ISSN 1476-9360

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Identification Number: 10.1080/01605682.2022.2077660


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.

Item Type: Article
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Additional Information: © 2021 Operational Research Society
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C63 - Computational Techniques
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C15 - Statistical Simulation Methods; Monte Carlo Methods; Bootstrap Methods
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Date Deposited: 04 Aug 2021 13:51
Last Modified: 16 Jun 2024 16:24

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