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Volatility can be detrimental to option values!

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  • Ghoddusi, Hamed
  • Fahim, Arash

Abstract

The value of digital options (both European and American types) can have an inverse-U shape relationship with the volatility of the underlying process! This seemingly counterintuitive proposition is driven by a particular feature of Martingale processes bounded from below (including the geometric Brownian motion (GBM) process). We show that in such processes a higher variance parameter may reduce the probability mass of realizations above the expected value. When the volatility approaches infinity, the probability of hitting a barrier above the mean goes to zero. Our finding is in contrast to the common belief that a higher volatility always increases all option values. Digital options are observed in a variety of economic applications, including mortgage tax, emission fines, venture capital, and credit risk models.

Suggested Citation

  • Ghoddusi, Hamed & Fahim, Arash, 2016. "Volatility can be detrimental to option values!," Economics Letters, Elsevier, vol. 149(C), pages 5-9.
    • Handle: RePEc:eee:ecolet:v:149:y:2016:i:c:p:5-9
    DOI: 10.1016/j.econlet.2016.10.001
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    Cited by:

    1. Ghoddusi, Hamed & Afkhami, Mohamad, 2019. "Valuation of mortgage interest deductibility under uncertainty: An option pricing approach," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 102-122.

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    More about this item

    Keywords

    Digital options; Hitting probability; Volatility; Non-monotone option value;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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