Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method

Lingling Xu, Hongjie Zhang and Fu Lee Wang ()
Additional contact information
Lingling Xu: School of Science and Technology, Hong Kong Metropolitan University, Hong Kong 999077, China
Hongjie Zhang: Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
Fu Lee Wang: School of Science and Technology, Hong Kong Metropolitan University, Hong Kong 999077, China

Mathematics, 2023, vol. 11, issue 3, 1-14

Abstract: Financial derivatives have developed rapidly over the past few decades due to their risk-averse nature, with options being the preferred financial derivatives due to their flexible contractual mechanisms, particularly Asian options. The Black–Scholes stock option pricing model is often used in conjunction with Monte Carlo simulations for option pricing. However, the Black–Scholes model assumes that the volatility of asset returns is constant, which does not square with practical financial markets. Additionally, Monte Carlo simulation suffers from slow error convergence. To address these issues, we first correct the asset volatility in the Black–Scholes model using a GARCH model. Then, the low error convergence rate of the Monte Carlo method is improved using variance reduction techniques. Meanwhile, the quasi-Monte Carlo approach based on low discrepancy sequences is used to refine the error convergence rate. We also provide a simulation experiment and result analysis to validate the effectiveness of our proposed method.

Keywords: Asian option pricing; GARCH model; Monte Carlo method; variance reduction technique; low-discrepancy sequence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/3/594/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/3/594/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:594-:d:1044657

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().