Free lesson · Technical analysis

Support, resistance and reversal: start with a price zone

Open interactive lesson Practice calculations Explore labs

Start with the idea

Support and resistance are candidate areas where price may react. A zone allows for measurement noise; it is not a barrier that must hold.

Symbols, units & horizon

C_t: completed closing price at bar t
K: previously fixed support/resistance level in price units
ATR_(t−1): positive prior average true range
z_t: distance in prior ATR multiples
ε: nonnegative zone half-width in ATR multiples
| |: absolute distance

When and why to use this

Use level distance as a continuous context feature, or as part of a predeclared touch, rejection or breakout rule.

Review the candlestick anatomy lesson first: real OHLC records prices, not the sequence of every trade.
Support: a candidate area below or near price. Resistance: a candidate area above or near price. The same level may play a different role after a break.
Choose levels from prior completed bars or confirmed pivots. Define the lookback, clustering tolerance, minimum touches and expiry before testing.
A reversal requires a specified change in direction, such as a completed close back above a reclaimed level after a decline. A wick alone is not a confirmed reversal.
Use a volatility-scaled distance to compare proximity across assets. A touch means entering a preset zone; it need not imply a fill.
A bounce rule and a breakout rule can trade opposite directions at the same level. Evaluate them as separate hypotheses.
Count repeated touches carefully: overlapping observations during one market event are not independent confirmations.

z_{t} = \frac{C_{t} - K}{A T R_{t - 1}}, | z_{t} | \leq ϵ

Specified chart rule · derivation and arithmetic

Support, resistance and reversal: start with a price zone

Subtract the fixed level from the observed close.
Divide by the strictly prior positive ATR to remove price scale.
For C=101,K=100,ATR=2, z=.5. A half-width ε=.6 includes this close because .5≤.6.

Work it by hand

The corresponding zone is K±εATR=100±1.2, or [98.8,101.2]. A close at 102 falls outside it.

Use the rule

Fix the definition, units and information timestamp.
Compute the example and inspect the graph.
Compare with a simple baseline on untouched periods after costs.

Before moving on

Write the exact rule, its availability time, an invalidation condition and a fair out-of-sample test.

Research checkpoint · reviewed 12 September 2026

Status: Finance and Stochastics, 2026; Warwick lists it as peer reviewed, in press. Repository abstract and publication metadata reviewed; proofs were not reviewed.
Scope: a theoretical stock-price model with three path-dependent states and linked buy/sell stopping problems. No empirical market sample or historical data dates are adopted here.
Connection: a chart boundary can become a state variable in a mathematical decision model. Its optimality depends on the assumed dynamics, rewards and risk preferences; it does not verify arbitrary chart levels.

Henderson, Jacka, Liu & Maeda · support/resistance and optimal stopping (2026) ↗

Research sources, review dates and limitations

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def level_distance(close,level,prior_atr,half_width=.6):
    if prior_atr<=0 or half_width<0: raise ValueError("Positive ATR and nonnegative width required")
    distance=(close-level)/prior_atr
    return distance,abs(distance)<=half_width

print(level_distance(101,100,2))

Continue learning

Technical Analysis: Geometry, Structure & Evidence — all lessons

Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations