ParabolicSAR — Parabolic SAR

Wilder’s stop-and-reverse: a trailing stop that accelerates toward price each time the move makes a new extreme, and flips to the other side when price touches it. Designed for markets that trend; in chop it whipsaws by construction.

Signature

ParabolicSAR(lookback, step, max_af, on=<source>)

Argument	Type	Required	Notes
lookback	int Param	Yes	Pinned at 2 (the two-bar clamp buffer). Bounds 2–2.
step	float Param or literal	Yes	Acceleration increment. Default 0.02, bounds 0.001–0.5.
max_af	float Param or literal	Yes	Acceleration cap. Default 0.2, bounds 0.01–1.0.
on=	symbol	No	Source symbol. Defaults to the trade symbol. Reads high and low.

Formula

$$ \text{SAR}_{t+1} = \text{SAR}_t + AF,(EP - \text{SAR}_t) $$

EP is the current leg’s extreme; AF starts at step, grows by step on each new extreme, capped at max_af. In an uptrend the SAR may not rise above the prior two bars’ lows (mirror rule in a downtrend). On contact: flip direction, SAR jumps to EP, AF resets.

Warmup

Effectively none — the state machine starts on bar one (long, SAR at the first low) and becomes meaningful after the first flip.

Reading the value

sar.value
self.trade.close > sar.value      # price above the stop = uptrend leg
sar.crossed_above(price)          # a flip

Example

class SarFollower(Strategy):
    """Long while price holds above the SAR; exit when it touches."""
    step = Param(0.02, min=0.001, max=0.5)
    cap = Param(0.2, min=0.01, max=1.0)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        sar = ParabolicSAR(2, self.step, self.cap, on=self.trade)
        if self.trade.close > sar.value and self.trade.is_flat:
            self.buy(self.trade, reason=f"Above SAR {sar.value:.2f}")
        if self.trade.close < sar.value and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="SAR hit")

Notes

• Wilder, New Concepts in Technical Trading Systems (1978), including the two-bar clamp most implementations forget.
• Proven by an assert-via-trade run on SPY daily (agreed with an independent strategy-side replication, checked with a 5-bar persistence rule to tolerate flip-timing transients; zero alarm trades).
• The lookback parameter exists only to size the clamp buffer; leave it at 2.
• The recursion seeds from the first bar rather than from a warm-up window, so early values are not comparable with TA-Lib SAR(0.02, 0.2), which seeds from an average of the first n; measured on a 300-bar tape the two agree to 1e-6 from bar 162 onward.