Models for Price Changes
In HF data, we can't just use "Returns = (P2-P1)/P1" because prices move in discrete steps (ticks). We use specialized Microstructure models.
1. Components of Price Change
We decompose an observed price change (Delta P) into two parts:
- Information Component: The "True" value change due to news. (Permanent).
- Noise Component: The Microstructure noise (Bid-Ask bounce, liquidity shocks). (Transitory).
Formula Concept: Observed Change = True Change + Noise
(Wait, I must avoid LaTeX blocks. Using plain text below)
Formula Concept: Observed Change = True Change + Noise
2. Ordered Probit Models (OPM)
Since price changes are discrete (e.g., -1 tick, 0 tick, +1 tick), we use Ordered Probit Models.
- Instead of predicting "Price will go up by 0.345%", we predict the Probability of a tick move.
- Output: "60% chance of +1 tick, 30% chance of 0 tick, 10% chance of -1 tick."
- Inputs: Order flow imbalance, Trade size, Duration since last trade.
3. Roll Model
A simple model proposed by Richard Roll (1984) to estimate the Effective Spread just from looking at the negative autocorrelation of returns.
- Logic: If price bounces are large, the spread must be wide.
- Formula: Correlates the covariance of consecutive returns to the Bid-Ask spread.
Why this matters: HFT algorithms use these models to predict the next tick. If the OPM model says "80% chance of +1 tick", the algo buys immediately to capture that spread.
Test Your Knowledge
Question 1 of 5
1. Why are standard regression models often unsuitable for tick-by-tick price changes?