After Black–Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed “why multifactor stochastic volatility models work so well”. Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Numerical methods on European option second order asymptotic expansions for multiscale stochastic volatility


    Beteiligte:
    Canhanga, Betuel (Autor:in) / Ni, Ying (Autor:in) / Rančić, Milica (Autor:in) / Malyarenko, Anatoliy (Autor:in) / Silvestrov, Sergei (Autor:in) / Sivasundaram, Seenith (Herausgeber:in)

    Kongress:

    ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences ; 2016 ; La Rochelle, France


    Erschienen in:

    Erscheinungsdatum :

    27.01.2017


    Format / Umfang :

    10 pages





    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Approximation methods of European option pricing in multiscale stochastic volatility model

    Ni, Ying / Canhanga, Betuel / Malyarenko, Anatoliy et al. | American Institute of Physics | 2017


    Pricing of Derivatives Option with Stochastic Prices Volatility

    Hengyu, W. / Jinxian, C. | British Library Online Contents | 2005


    The use of asymptotic expansions to enhance computational methods

    Merkle, Charles / Venkateswaran, Sankaran | AIAA | 1998


    The Use of Asymptotic Expansions to Enhance Computational Methods

    Merkle, C. L. / Venkateswaran, S. / AIAA | British Library Conference Proceedings | 1998