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Simple approximations for option pricing under mean reversion and stochastic volatility

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Abstract

This paper provides simple approximations for evaluating option prices and implied volatilities under stochastic volatility. Simple recursive formulae are derived that can easily be implemented in spreadsheets. The traditional random walk assumption, dominating in the analysis of financial markets, is compared with mean reversion which is often more relevant in commodity markets. Deterministic components in the mean and volatility are taken into consideration to allow for seasonality, another frequent aspect of commodity markets. The stochastic volatility is suitably modelled by GARCH. An application to electricity options shows that the choice between a random walk and a mean reversion model can have strong effects for predictions of implied volatilities even if the two models are statistically close to each other.

Suggested Citation

  • Hafner, C.M., 2003. "Simple approximations for option pricing under mean reversion and stochastic volatility," Econometric Institute Research Papers EI 2003-20, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1720
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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
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    More about this item

    Keywords

    derivatives; energy markets; mean reversion; seasonality; spreadsheets; stochastic volatility;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric 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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