Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Betuel Canhanga (), Anatoliy Malyarenko (), Jean-Paul Murara (), Ying Ni () and Sergei Silvestrov ()
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Betuel Canhanga: Eduardo Mondlane University
Anatoliy Malyarenko: Mälardalen University
Jean-Paul Murara: Mälardalen University
Ying Ni: Mälardalen University
Sergei Silvestrov: Mälardalen University

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 4, 1075-1087

Abstract: 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).

Keywords: Financial market; Mean reversion volatility; Asymptotic expansion; Stochastic volatilities; Regular perturbation; Singular perturbation; European option; 91G20; 91G60; 91G80 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11009-017-9553-8

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