Non-Gaussian GARCH option pricing models and their diffusion limits

Item Type Journal paper
Abstract This paper investigates the weak convergence of general non-Gaussian GARCH models together with an application to the pricing of European style options determined using an extended Girsanov principle and a conditional Esscher transform as the pricing kernel candidates. Applying these changes of measure to asymmetric GARCH models sampled at increasing frequencies, we obtain two risk neutral families of processes which converge to different bivariate diffusions, which are no longer standard Hull–White stochastic volatility models. Regardless of the innovations used, the GARCH implied diffusion limit based on the Esscher transform can be obtained by applying the minimal martingale measure under the physical measure. However, we further show that for skewed GARCH driving noise, the risk neutral diffusion limit of the extended Girsanov principle exhibits a non-zero market price of volatility risk which is proportional to the market price of the equity risk, where the constant of proportionality depends on the skewness and kurtosis of the underlying distribution. Our theoretical results are further supported by numerical simulations and a calibration exercise to observed market quotes.
Authors Badescu, Alexandru; Elliott, Robert & Ortega, Juan-Pablo
Journal or Publication Title European journal of operational research : EJOR
Language English
Subjects finance
HSG Classification contribution to scientific community
HSG Profile Area SEPS - Quantitative Economic Methods
Refereed Yes
Date 16 December 2015
Publisher Elsevier
Place of Publication Amsterdam [u.a.]
Volume 247
Number 3
Page Range 820-830
ISSN 0377-2217
ISSN-Digital 1872-6860
Publisher DOI https://doi.org/10.1016/j.ejor.2015.06.046
Depositing User Prof. Ph.D Juan-Pablo Ortega Lahuerta
Date Deposited 21 Nov 2016 18:29
Last Modified 20 Jul 2022 17:29
URI: https://www.alexandria.unisg.ch/publications/249737

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Badescu, Alexandru; Elliott, Robert & Ortega, Juan-Pablo (2015) Non-Gaussian GARCH option pricing models and their diffusion limits. European journal of operational research : EJOR, 247 (3). 820-830. ISSN 0377-2217

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https://www.alexandria.unisg.ch/id/eprint/249737
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