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  • 1.
    Wu, Desheng
    et al.
    Stockholm University, Faculty of Social Sciences, Stockholm Business School. University of Chinese Academy of Sciences, China.
    Liu, Tianxiang
    Curve Fitting Method for Implied Volatility2018In: Journal of Derivatives, ISSN 1074-1240, E-ISSN 2168-8524, Vol. 26, no 2, p. 19-37Article in journal (Refereed)
    Abstract [en]

    Curve-fitting methods are widely used in derivatives markets for construction of the implied volatility surface (IVS). Here we discuss the goodness of fit, smoothness, and economic implications of 12 distinctive curve-fitting methods. The choice of method relies on specific requirements. When fitting the Chicago Board Options Exchange data, three interpolation methods were found to provide the best goodness, whereas quadratic regression, the Nadaraya–Watson kernel regression, and the theoretical Carr–Wu model generate the smoothest surfaces. Because of the irregular nature of the emerging options market data, we propose a transformation method to improve three statistical methods to satisfy the Lee’s condition. Empirically, quadratic regression provides the best goodness when fitting the China 50ETF options data. In addition, the Carr–Wu model is a very good alternative because it natively satisfies the Lee’s condition and has economic implications.

  • 2.
    Wu, Desheng
    et al.
    Stockholm University, Faculty of Social Sciences, Stockholm Business School. University of Chinese Academy of Sciences, China.
    Liu, Tianxiang
    New Approach to Estimating VIX Truncation Errors Using Corridor Variance Swaps2018In: Journal of Derivatives, ISSN 1074-1240, E-ISSN 2168-8524, Vol. 25, no 4, p. 54-70Article in journal (Refereed)
    Abstract [en]

    An approach to estimating the volatility index (VIX) truncation error using corridor variance swaps (CVSs) is developed. It is shown that the existing VIX approach significantly underestimates option volatility in emerging markets. The truncation error of iVX (a product that mimics VIX in China's options market) is not only significant, but also volatile under different market conditions. It is demonstrated that other emerging markets, such as Korea and Mexico, also have significant VIX truncation errors. A new approach, different from the popular Fast Fourier Transform (FFT), is proposed for the valuation of corridor variance swaps. The Feynman-Kac connection is employed to derive a closed-form result and avoid the arbitrary damping factor (alpha) problem in the FFT approach.

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