Methodology and Computing in Applied Probability

, Volume 19, Issue 4, pp 1075–1087 | Cite as

Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

  • Betuel CanhangaEmail author
  • Anatoliy Malyarenko
  • Jean-Paul Murara
  • Ying Ni
  • Sergei Silvestrov


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).


Financial market Mean reversion volatility Asymptotic expansion Stochastic volatilities Regular perturbation Singular perturbation European option 

Mathematics Subject Classification (2010)

91G20 91G60 91G80 


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This work was partially supported by Swedish SIDA Foundation - International Science Program. Betuel Canhanga and Jean-Paul Murara thank Division of Applied Mathematics, School of Education, Culture and Communication, Malardalen University for creating excellent research and educational environment.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Betuel Canhanga
    • 1
    Email author
  • Anatoliy Malyarenko
    • 2
  • Jean-Paul Murara
    • 2
  • Ying Ni
    • 2
  • Sergei Silvestrov
    • 2
  1. 1.DMIEduardo Mondlane UniversityMaputoMozambique
  2. 2.UKKMälardalen UniversityVästeråsSweden

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