VPIN Toxic Flow Detection

Problem

VPIN (Volume-Synchronized Probability of Informed Trading) estimates the probability of toxic (informed) order flow. Given buy and sell volumes across multiple volume buckets, compute:

$\text{VPIN} = \frac{|V_{\text{buy}} - V_{\text{sell}}|}{V_{\text{buy}} + V_{\text{sell}}}$

where $V_{\text{buy}} = \sum_i v_i^{\text{buy}}$ and $V_{\text{sell}} = \sum_i v_i^{\text{sell}}$ are the total buy and sell volumes across all buckets.

Input Format

A single line: buy_volumes sell_volumes where each is a comma-separated list of floats.

Output Format

A single value: VPIN, to 4 decimal places.