On the Curvature of the Bachelier Implied Volatility
Using Malliavin calculus, the paper derives ATM curvature formulas for Bachelier implied volatility in correlated, fractional stochastic volatility models.
What it examines
This paper studies the at‐the‐money curvature of Bachelier implied volatility using Malliavin calculus. It extends classical models to account for negative prices and stochastic volatility, including fractional cases. The approach computes short-term curvature and second-order Greeks, helping better understand and capture market smile dynamics.
What it concludes
The study derives a formula for short-term at‐the‐money Bachelier curvature using Malliavin calculus. Results show curvature depends on volatility roughness and model parameters. Applications include improved risk management, derivative pricing, and calibration in markets with negative prices. Future research can test additional models and validate these findings empirically.
Evidence objects
The study employs advanced mathematics via Malliavin calculus to analyze at-the-money curvature of Bachelier implied volatility, splitting it into two distinct components from uncorrelated dynamics and correlation with fractional volatility.
key_findings bullet 1 · key_findings · validation V0
A notable finding reveals that short-term curvature is sensitive to the Hurst parameter ($H$), where increased roughness generates significant divergences in option pricing sensitivities, impacting second-order Greeks for risk management.
key_findings bullet 2 · key_findings · validation V0
New formulations for Malliavin derivatives on non-Markovian volatility broaden analytical scope to models including commodities and negative-price markets, while gradient descent optimizations highlight theoretical breakthroughs and practical challenges for practitioners.
key_findings bullet 3 · key_findings · validation V0
This paper analyzes the curvature of the $$\text{Bachelier implied volatility}$$ within derivative modeling, presenting fresh perspectives for pricing and risk management. Its novel approach introduces ideas that challenge paradigms, making it an intriguing read despite appearing moderately incremental. Overall, readers interested in volatility studies may find its methodology uniquely compelling.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
- … The presented results can be an interesting tool in financial modeling and in the computation of the corresponding Greeks. Moreover, they allow us to obtain general …
Source row: 1465 · abstract type: snippet