Conditional Optimality in Directional Volatility Capture

We develop an optimization framework that yields the Directional Volatility 
Capture allocation, a threshold rule that maps directional-volatility estimates to 
position size. Our theoretical model establishes optimal allocation rules that 
maintain portfolio solvency while capturing directional volatility across bounded 
Itô diffusions. We prove that threshold-based allocation rules uniquely maximize 
expected log-wealth under total-variation costs.

Empirical validation across 26 assets demonstrates a 69% win rate with 16.0% median annualized log-
growth improvement when signal detection conditions are effective. The 
framework provides practical implementation guidelines for automated market 
makers and portfolio managers seeking to harvest volatility premiums while 
managing downside risk.

Preprint; submitted to Quantitative Finance (Taylor & Francis), Aug 2025; under review.