Cao, Z.; Zhao, S.; Huang, S. One-X Property Conjecture, Stochastic Orders and Implied Volatility Surface Construction. Preprints2024, 2024091533. https://doi.org/10.20944/preprints202409.1533.v1
APA Style
Cao, Z., Zhao, S., & Huang, S. (2024). One-X Property Conjecture, Stochastic Orders and Implied Volatility Surface Construction. Preprints. https://doi.org/10.20944/preprints202409.1533.v1
Chicago/Turabian Style
Cao, Z., Siqiao Zhao and Shaosai Huang. 2024 "One-X Property Conjecture, Stochastic Orders and Implied Volatility Surface Construction" Preprints. https://doi.org/10.20944/preprints202409.1533.v1
Abstract
In this work, we explore Conjecture 1 proposed in the newly released pioneering paper “Volatility transformers: an optimal transport-inspired approach to arbitrage-free shaping of implied volatility surfaces” by Zetocha Valer, which posits that the “One-X” property is both a necessary and sufficient condition for convex order between non-negative continuous strictly increasing distributions with the same mean. We provide a counterexample demonstrating that the conjecture, as originally stated, does not hold. By examining stochastic orders, particularly the increasing convex order, and the “One-X” property, we propose an enhanced version of the conjecture which is shown to be valid. Furthermore, we discuss the implications of these findings in the context of equity implied volatility fitting and the construction of implied volatility surfaces, highlighting the challenges posed by real-market conditions. In the end, we propose several applications in implied volatility surface construction or simulation.
Keywords
Convex order, "One-X" property, imported volatility, synthetic data generation, stop-loss order
Subject
Business, Economics and Management, Finance
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
