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Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique. (MAM)ORCID iD: 0000-0001-8361-4152
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0835-7536
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-9635-0301
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2018 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 6, p. 1328-1349Article in journal (Refereed) Published
Abstract [en]

The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.

Place, publisher, year, edition, pages
Taylor & Francis, 2018. Vol. 47, no 6, p. 1328-1349
Keywords [en]
stochastic volatility,  option pricing,  asymptotic expansion
National Category
Probability Theory and Statistics Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-36595DOI: 10.1080/03610926.2017.1318923ISI: 000423714800004Scopus ID: 2-s2.0-85031106499OAI: oai:DiVA.org:mdh-36595DiVA, id: diva2:1145934
Funder
Sida - Swedish International Development Cooperation AgencyAvailable from: 2017-10-01 Created: 2017-10-01 Last updated: 2018-02-08Bibliographically approved

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Publisher's full textScopushttp://www.tandfonline.com/doi/full/10.1080/03610926.2017.1318923

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Canhanga, BetuelMalyarenko, AnatoliyNi, YingRancic, MilicaSilvestrov, Sergei
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