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Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility
DMI, Eduardo Mondlane University, Maputo, Mozambique.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)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0835-7536
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2017 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, 1075-1087 p.Article in journal (Refereed) Published
Abstract [en]

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).

Place, publisher, year, edition, pages
Springer, 2017. Vol. 19, no 4, 1075-1087 p.
Keyword [en]
Financial market, Mean reversion volatility, Asymptotic expansion,  Stochastic volatilities, Regular perturbation, Singular perturbation, European option
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-36594DOI: 10.1007/s11009-017-9553-8ISI: 000413792200005OAI: oai:DiVA.org:mdh-36594DiVA: diva2:1145933
Conference
15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2017-10-01 Created: 2017-10-01 Last updated: 2017-11-16Bibliographically approved

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Publisher's full texthttps://doi.org/10.1007/s11009-017-9553-8

Authority records BETA

Malyarenko, AnatoliyNi, YingSilvestrov, Sergei

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