Abstract
The Hagan et al SABR implied volatility approximation formula can result in a negative probability density function when applied to long-dated options. This paper presents a methodology for avoiding that problem by writing the density function as the sum of two components that are always positive. One component corresponds to the absorbing boundary at F = 0, which can be a significant part of the density function for long-dated options. An upper bound on the time to expiry for the Hagan et al formula is also derived, which shows that their formula cannot be expected to work as this upper bound is approached.
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
