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Modeling Of Returns And Option Pricing Using Models With Flexible Volatility

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  • Pavel Vaněček

Abstract

This work deals with time series with flexible conditional variance which is changing according to past observations and values of past volatilities. We consider a class of ARCH-type models as a special case of GARCH models and its extension GARCH-M Stationarity, estimation procedures, and LM tests are discussed. Further, we apply the models to financial data from the Czech capital market forecasting stock returns and estimating option prices. We present an extension of option pricing using equivalent martingale measure which special case leads to the well-known Black-Scholes formula.

Suggested Citation

  • Pavel Vaněček, 2003. "Modeling Of Returns And Option Pricing Using Models With Flexible Volatility," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 10(19).
  • Handle: RePEc:czx:journl:v:10:y:2003:i:19:id:126
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    File URL: http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/126
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    More about this item

    Keywords

    Black-Scholes formula; GARCH; martingale measure; volatility;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G - Financial Economics

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