Learning for infinitely divisible GARCH models in option pricing

Zhu Fumin (), Bianchi Michele Leonardo (), Kim Young Shin (), Fabozzi Frank J. () and Wu Hengyu ()
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Zhu Fumin: College of Economics, Center for Finance & Accounting Research, Shenzhen University, Shenzhen, Guangdong, China
Bianchi Michele Leonardo: Regulation and Macroprudential Analysis Directorate, Bank of Italy, Rome, Italy
Kim Young Shin: College of Business, Stony Brook University, Stony Brook, NY, USA
Fabozzi Frank J.: EDHEC Business School, Nice, France
Wu Hengyu: Management School, Jinan University, Guangzhou, Guangdong, China

Studies in Nonlinear Dynamics & Econometrics, 2020, vol. 25, issue 3, 35-62

Abstract: This paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

Keywords: Lévy–GARCH models; Markov chain Monte Carlo; option pricing; particle filtering; sequential Bayesian learning (search for similar items in EconPapers)
JEL-codes: G11 G12 G13 G17 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/snde-2019-0088

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