The research question
How do changes in the implied-volatility surface relate to subsequent price dynamics? Which changes coincide with, precede or follow abrupt price movements, and how does liquidity affect that relationship?
This is an ongoing research direction connecting mathematical finance, financial time series and market microstructure. This note describes the questions and intended approach; it does not report completed empirical findings.
Define the event before fitting the model
An initial challenge is to define a price burst consistently. The definition needs an observation horizon, a reference for the size of the move and a treatment of repeated or overlapping events.
Those choices determine which episodes are included. They must be made explicit before comparing model results.
Investigate transmission and amplification
The research considers changes in volatility conditions alongside a dynamically evolving liquidity landscape. One question is whether liquidity conditions help explain where a shock is transmitted or amplified.
Liquidity maps are a possible input to investigate. An observed association would still need to be separated from a causal explanation.
A disciplined quantitative approach
The intended approach connects transparent event definitions, time alignment and comparison across market conditions. Statistical models and machine learning can be assessed against simpler baselines, with evaluation on observations not used to fit the models.
The objective is to understand the stability and usefulness of a relationship, including the circumstances in which it weakens.
Connection to investment tools
This agenda informs our broader interest in risk, systematic investment methods and portfolio monitoring. Any operational application would require its own validation.
Future notes can document the event definition, data construction and empirical results as the research develops.