Volatility can be detrimental to option values!

Hamed Ghoddusi and Arash Fahim

Economics Letters, 2016, vol. 149, issue C, 5-9

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.

Keywords: Digital options; Hitting probability; Volatility; Non-monotone option value (search for similar items in EconPapers)
JEL-codes: C63 G13 G17 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:149:y:2016:i:c:p:5-9

DOI: 10.1016/j.econlet.2016.10.001

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