The Physical Crash Frontier: What Finite Option Quotes Can and Cannot Reveal

Jirong Zhuang

Papers from arXiv.org

Abstract: Physical crash probabilities recovered from option prices depend on a pricing kernel and on a risk-neutral distribution that finitely many bid and ask quotes do not identify. For a power utility investor, we characterize the pairs of physical crash probability and expected loss below the crash threshold that the quotes admit; the boundary of this set is the physical crash frontier. Both coordinates are ratios of moments, yet when the index is bounded above the set is convex, and second-order cone programs compute it exactly at the calibrated risk aversion of two. In a decade of weekly S&P 500 cross sections, the quotes beyond the two puts nearest a 10 percent decline shrink the range of admissible crash probabilities by about 80 percent, yet its upper end remains two to three times its lower end. That lower end exists only because the index is bounded. Otherwise, for any investor more risk averse than the log investor, a vanishing probability far in the right tail inflates the denominator and drives the crash probability to zero while every quote stays inside its spread. A positive floor is therefore a joint statement about prices and a tail restriction; anything tighter than the frontier is an assumption.

Date: 2026-08, Revised 2026-09
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2608.23274 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2608.23274

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().