13 Pages Posted: 12 Sep 2016 Last revised: 16 Jan 2017
Date Written: September 10, 2016
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 Maringale processes bounded from below (including both the Geometric Brownian Motion (GBM) and the CIR processes). 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 increases all option values. Digital options are observed in a variety of economics applications, including mortgage tax, emission fines, venture capital, and credit risk models.
Keywords: Digital Options, Hitting Probability, Volatility, Non-Monoton Option Value
JEL Classification: G13, G17, C63
Suggested Citation: Suggested Citation
Ghoddusi, Hamed and Fahim, Arash, Volatility Can Be Detrimental to Option Values! (September 10, 2016). Stevens Institute of Technology School of Business Research Paper No. 2837292. Available at SSRN: https://ssrn.com/abstract=2837292