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Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Author

Listed:
  • Betuel Canhanga

    (Eduardo Mondlane University)

  • Anatoliy Malyarenko

    (Mälardalen University)

  • Jean-Paul Murara

    (Mälardalen University)

  • Ying Ni

    (Mälardalen University)

  • Sergei Silvestrov

    (Mälardalen University)

Abstract

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).

Suggested Citation

  • Betuel Canhanga & Anatoliy Malyarenko & Jean-Paul Murara & Ying Ni & Sergei Silvestrov, 2017. "Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1075-1087, December.
  • Handle: RePEc:spr:metcap:v:19:y:2017:i:4:d:10.1007_s11009-017-9553-8
    DOI: 10.1007/s11009-017-9553-8
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    References listed on IDEAS

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    1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
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