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Retrieving risk neutral moments and expected quadratic variation from option prices

Author

Listed:
  • Leonidas S. Rompolis

    (Athens University of Economics and Business)

  • Elias Tzavalis

    (Athens University of Economics and Business)

Abstract

This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange.

Suggested Citation

  • Leonidas S. Rompolis & Elias Tzavalis, 2017. "Retrieving risk neutral moments and expected quadratic variation from option prices," Review of Quantitative Finance and Accounting, Springer, vol. 48(4), pages 955-1002, May.
    • Handle: RePEc:kap:rqfnac:v:48:y:2017:i:4:d:10.1007_s11156-016-0575-z
    DOI: 10.1007/s11156-016-0575-z
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    2. Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.
    3. Carol Alexander & Johannes Rauch, 2017. "The Aggregation Property and its Applications to Realised Higher Moments," Papers 1709.08188, arXiv.org.

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    More about this item

    Keywords

    Risk neutral moments; Characteristic function; Expected quadratic variation; Jump component;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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