Constructing a mobility oscillator from price distributions

Congestion and a data-shaped histogram

Congestion is a lookback region where price spends disproportionate time. A longer stay or a more recent stay is treated as more significant, and the resulting distribution peak is later treated as a reference zone.

The working hypothesis is that prices move more freely where the distribution is small and more slowly where the distribution is large.

Unlike a lognormal options-pricing assumption, these distributions are tabular histograms. Their shape is taken from the data rather than from a fixed functional form.

Build the lookback price-distribution function

A lookback price-distribution function is built from the period minimum low to the maximum high and split into equal intervals. It uses the same high-low window as a stochastic oscillator.

That function is the empirical frequency of price action across those equal bins. No parametric shape is assumed.

Recover bin frequencies from the cumulative function

Bin frequencies equal adjacent differences of a cumulative price-distribution function that treats each bar as uniformly distributed between its high and low.

The cumulative price-distribution function is the running fraction of lookback price action at or below each bin boundary. Adjacent differences of that cumulative record recover the binned frequencies.

Turn the bins into a signed mobility oscillator

The price-mode is the center of the bin with the largest distribution value during the lookback.

The mobility oscillator equals 100 times one minus the current-bin frequency over the modal-bin frequency. It is signed by whether the close is above or below the price-mode, and it is bounded from -100 to +100. Sparse bins map as high mobility and dense bins map as low mobility.

Illustrated lookback, bins, and a slow mobility oscillator

Illustrated constructions used a 14-bar lookback, 10 or 20 equal bins, and a seven-bar exponential average of the oscillator.

That exponentially smoothed series is the slow mobility oscillator. It is used to read trend direction and crossings.

Base-building in a stepped advance

In a stepped advance, breathing pauses that rebuild congestion and return the oscillator to zero are described as base-building before the next upward step.

Base-building is a pause in which congestion rebuilds and the oscillator returns toward zero before the next directional step.

A directional check and a two-sided overlay

When a break from congestion is expected but direction is unknown, one overlay is an options straddle. A stochastic oscillator is the companion used to assign direction.

The stochastic oscillator is range-normalized and shares the same high-low lookback window as the price-distribution function. The options straddle is a two-sided options overlay used when a mobility break is expected but direction is not specified.