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On Estimation of Volatility Surface and Prediction of Future Spot Volatility

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  • Fima Klebaner
  • Truc Le
  • Robert Liptser
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    Abstract

    A stochastic process v(t) is considered as a model for asset's spot volatility. A new approach is introduced for predicting future spot volatility and future volatility surface using a finite set of observed option prices. When the volatility parameter σ2 in the Black-Scholes formula[image omitted]   is represented by the integrated volatility [image omitted]   , then the local volatility surface can be estimated. The main idea is to linearize the expressions for implied volatility by using a result on Normal correlation. This linearization is obtained by introducing various ad hoc approximations.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 13 (2006)
    Issue (Month): 3 ()
    Pages: 245-263

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    Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:245-263

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    1. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    2. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. Ram Bhar & Carl Chiarella & Nadima El-Hassan & Xiaosu Zheng, 2000. "The Reduction of Forward Rate Dependent Volatility HJM Models to Markovian Form: Pricing European Bond Option," Research Paper Series 36, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Laurence K. Eisenberg & Robert A. Jarrow, 1991. "Option pricing with random volatilities in complete markets," Working Paper 91-16, Federal Reserve Bank of Atlanta.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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    Cited by:
    1. Vyacheslav Abramov & Fima Klebaner, 2007. "Estimation and Prediction of a Non-Constant Volatility," Asia-Pacific Financial Markets, Springer, vol. 14(1), pages 1-23, March.
    2. Sabiruzzaman, Md. & Monimul Huq, Md. & Beg, Rabiul Alam & Anwar, Sajid, 2010. "Modeling and forecasting trading volume index: GARCH versus TGARCH approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 141-145, May.

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