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Discrete Time Hedging of OTC Options in a GARCH Environment: A Simulation Experiment

Author

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  • Hagerud, Gustaf E.

    (Department of Finance)

Abstract

This paper examines the effect of using Black and Scholes formula for pricing and hedging options in a discrete time heteroskedastic environment. This is done by a simulation procedure where asset returns are generated from a GARCH (1,1)-t model. In the simulation a hypothetical trader writes an option and then delta- hedges his position until the option expires. It is shown that the variance of the returns on the hedged position is considerably higher in a GARCH (1,1) environment than in a homoskedastic environment. The variance of returns depends greatly on the level of kurtosis in the returns process and on the first-order autocorrelation in centered and squared returns.

Suggested Citation

  • Hagerud, Gustaf E., 1997. "Discrete Time Hedging of OTC Options in a GARCH Environment: A Simulation Experiment," SSE/EFI Working Paper Series in Economics and Finance 165, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0165
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    More about this item

    Keywords

    GARCH; option pricing; Black and Scholes formula; Monte Carlo experiment;
    All these keywords.

    JEL classification:

    • 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

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